# Straight Lines and Pair of Straight Lines · Mathematics · MHT CET

Start Practice## MCQ (Single Correct Answer)

MHT CET 2023 14th May Evening Shift

Let $$P \equiv(-3,0), Q \equiv(0,0)$$ and $$R \equiv(3,3 \sqrt{3})$$ be three points. Then the equation of the bisector of the angle $$\mathrm{PQR}$$ ...

MHT CET 2023 14th May Evening Shift

The centroid of the triangle formed by the lines $$x+3 y=10$$ and $$6 x^2+x y-y^2=0$$ is

MHT CET 2023 14th May Morning Shift

$$\mathrm{p}$$ is the length of perpendicular from the origin to the line whose intercepts on the axes are a and $$\mathrm{b}$$ respectively, then $$\...

MHT CET 2023 14th May Morning Shift

The perpendiculars are drawn to lines $$L_1$$ and $$L_2$$ from the origin making an angle $$\frac{\pi}{4}$$ and $$\frac{3 \pi}{4}$$ respectively with ...

MHT CET 2023 13th May Evening Shift

Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $$2 x+y=3$$, then the combined ...

MHT CET 2023 13th May Evening Shift

$$P S$$ is the median of the triangle with vertices at $$P(2,2), Q(6,-1)$$ and $$R(7,3)$$, then the intercepts on the coordinate axes of the line pass...

MHT CET 2023 13th May Morning Shift

If the angle between the lines given by $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0$$ is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then the val...

MHT CET 2023 13th May Morning Shift

The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the length (in units) of the side o...

MHT CET 2023 13th May Morning Shift

A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that it forms a $$\triangle \mathrm...

MHT CET 2023 12th May Evening Shift

If the pair of lines given by $$(x \cos \alpha+y \sin \alpha)^2=\left(x^2+y^2\right) \sin ^2 \alpha$$ are perpendicular to each other, then $$\alpha$$...

MHT CET 2023 12th May Evening Shift

If $$\mathrm{k}_{\mathrm{i}}$$ are possible values of $$\mathrm{k}$$ for which lines $$\mathrm{k} x+2 y+2=0,2 x+\mathrm{k} y+3=0$$ and $$3 x+3 y+\math...

MHT CET 2023 12th May Morning Shift

The co-ordinates of the points on the line $$2 x-y=5$$ which are the distance of 1 unit from the line $$3 x+4 y=5$$ are

MHT CET 2023 12th May Morning Shift

Let $$\mathrm{PQR}$$ be a right angled isosceles triangle, right angled at $$\mathrm{P}(2,1)$$. If the equation of the line $$\mathrm{QR}$$ is $$2 x+y...

MHT CET 2023 11th May Evening Shift

The joint equation of the lines pair of lines passing through the point $$(3,-2)$$ and perpendicular to the lines $$5 x^2+2 x y-3 y^2=0$$ is

MHT CET 2023 11th May Morning Shift

If the angle between the lines represented by the equation $$x^2+\lambda x y-y^2 \tan ^2 \theta=0$$ is $$2 \theta$$, then the value of $$\lambda$$ is...

MHT CET 2023 11th May Morning Shift

$$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b}$$ and the line passes throug...

MHT CET 2023 10th May Evening Shift

The joint equation of a pair of lines passing through the origin and making an angle of $$\frac{\pi}{4}$$ with the line $$3 x+2 y-8=0$$ is

MHT CET 2023 10th May Evening Shift

Two sides of a square are along the lines $$5 x-12 y+39=0$$ and $$5 x-12 y+78=0$$, then area of the square is

MHT CET 2023 10th May Morning Shift

The number of integral values of $$\mathrm{p}$$ in the domain $$[-5,5]$$, such that the equation $$2 x^2+4 x y-p y^2+4 x+q y+1=0$$ represents pair of ...

MHT CET 2023 10th May Morning Shift

The points $$(1,3),(5,1)$$ are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line $$y=2 x+\mathrm{c}$$, then on...

MHT CET 2023 9th May Evening Shift

If the slope of one of the lines represented by $$a x^2+(2 a+1) x y+2 y^2=0$$ is reciprocal of the slope of the other, then the sum of squares of slop...

MHT CET 2023 9th May Evening Shift

The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular to the line from the origin mak...

MHT CET 2023 9th May Morning Shift

If the distance between the parallel lines given by the equation $$x^2+4 x y+p y^2+3 x+q y-4=0$$ is $$\lambda$$, then $$\lambda^2=$$

MHT CET 2023 9th May Morning Shift

The distance of a point $$(2,5)$$ from the line $$3 x+y+4=0$$ measured along the line $$L_1$$ and $$L_1$$ are same. If slope of line $$L_1$$ is $$\fra...

MHT CET 2022 11th August Evening Shift

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y = 5$$ is

MHT CET 2022 11th August Evening Shift

The equations of the lines passing through the point $$(3,2)$$ and making an acute angle of $$45^{\circ}$$ with the line $$x-2 y-3=0$$ are

MHT CET 2021 24th September Evening Shift

If the polar co-ordinates of a point are $$\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)$$, then its Cartesian co-ordinates are

MHT CET 2021 24th September Evening Shift

The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is

MHT CET 2021 24th September Evening Shift

If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{K}$$ are

MHT CET 2021 24th September Evening Shift

The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

MHT CET 2021 24th September Morning Shift

If the lines respresented by $$a x^2-b x y-y^2=0$$ make angle $$\alpha$$ and $$\beta$$ with the positive direction of $$\mathrm{X}$$-axis, then $$\tan...

MHT CET 2021 24th September Morning Shift

If the angle between the lines is $$\frac{\pi^{\mathrm{C}}}{4}$$ and slope of one of the lines is $$\frac{1}{2}$$, then slope of the other line is...

MHT CET 2021 24th September Morning Shift

If one of the lines given by $$k x^2+x y-y^2=0$$ bisect the angle between the co-ordinate axes then the values of $$k$$ are

MHT CET 2021 23rd September Evening Shift

The joint equation of pair of lines through the origin and having slopes $$(1+\sqrt{2})$$ and $$\frac{1}{(1+\sqrt{2})}$$ is

MHT CET 2021 23rd September Evening Shift

If $$4 a b=3 h^2$$, then the ratio of slopes of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is

MHT CET 2021 23rd September Evening Shift

The distance between the lines $$3 x+4 y=9$$ and $$6 x+8 y=15$$ is

MHT CET 2021 23rd September Evening Shift

If the slopes of the lines given by the equation $$a x^2+2 h x y+b y^2=0$$ are in the ratio $$5: 3$$, then the ratio $$h^2: a b=$$

MHT CET 2021 23th September Morning Shift

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with th...

MHT CET 2021 23th September Morning Shift

If two lines represented by $$a x^2+2 h x y+b y^2=0$$ makes angles $$\alpha$$ and $$\beta$$ with positive direction of $$\mathrm{X}$$-axis, then $$\ta...

MHT CET 2021 23th September Morning Shift

The combined equation of a pair of lines passing through the origin and inclined at $$60^{\circ}$$ and $$30=$$ respectively with $$x$$-axis is

MHT CET 2021 22th September Evening Shift

If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a =

MHT CET 2021 22th September Evening Shift

If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockwise direction through an angle...

MHT CET 2021 22th September Evening Shift

If lines represented by the equation $$\mathrm{px}^2-\mathrm{qy^{2 }}=0$$ are distinct, then

MHT CET 2021 22th September Morning Shift

If slope of one of the lines ax$$^2$$ + 2hxy + by$$^2$$ = 0 is twice that of the other, then h$$^2$$ : ab is

MHT CET 2021 22th September Morning Shift

Area of the triangle formed by the lines $$y^2-9 x y+18 x^2=0$$ and $$y=9$$ is

MHT CET 2021 22th September Morning Shift

The equation of perpendicular bisector of the line segment joining $$A(-2,3)$$ and $$B(6,-5)$$ is

MHT CET 2021 21th September Evening Shift

If $$\mathrm{(m+3 n)(3 m+n)=4 h^2}$$, then the acute angle between the lines represented by $$\mathrm{m x^2+2 h x y+n y^2=0}$$ is

MHT CET 2021 21th September Evening Shift

If $$\mathrm{p}$$ is the length of the perpendicular from origin to the line whose intercepts on the axes are a and $$b$$, then $$\frac{1}{a^2}+\frac{...

MHT CET 2021 21th September Evening Shift

If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+\cot^2\beta=$$

MHT CET 2021 21th September Morning Shift

If the two lines given by $$a x^2+2 h x y+b y^2=0$$ make inclinations $$\propto$$ and $$\beta$$, then $$\tan (\alpha+\beta)=$$

MHT CET 2021 21th September Morning Shift

If the polar co-ordinates of a point are $$\left(\sqrt{2}, \frac{\pi}{4}\right)$$, then its Cartesian co-ordinates are

MHT CET 2021 21th September Morning Shift

The equation of a line passing through $$(\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)$$ ) and making an angle $$(90+\propto)$$ with positive dir...

MHT CET 2021 21th September Morning Shift

The product of the perpendicular distances from $$(2,-1)$$ to the pair of lines $$2 x^2-5 x y+2 y^2=0$$ is

MHT CET 2021 20th September Evening Shift

The x-intercept of a line passing through the points $$\left(\frac{-1}{2}, 1\right)$$ and (1, 2) is :

MHT CET 2021 20th September Evening Shift

If the equation $$3x^2-kxy-3y^2=0$$ represents the bisectors of angles between the lines $$x^2-3xy-4y^2=0$$, then value of k is

MHT CET 2021 20th September Evening Shift

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y=3$$ is

MHT CET 2021 20th September Morning Shift

If the acute angle between the lines given by $$\mathrm{a x^2+2 h x y+b y^2=0}$$ is $$\frac{\pi}{4}$$, then $$\mathrm{4 h^2=}$$

MHT CET 2021 20th September Morning Shift

The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $$x=3$$ is

MHT CET 2021 20th September Morning Shift

The slope of the line through the origin which makes an angle of 30$$^\circ$$ with the positive direction of Y-axis measured anticlockwise is :

MHT CET 2020 16th October Morning Shift

If the equation $$k x y+5 x+3 y+2=0$$ represents a pair of lines, then $$k=$$

MHT CET 2020 16th October Morning Shift

If $$(a,-2 a), a>0$$ is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is

MHT CET 2020 16th October Morning Shift

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$,...