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

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 $$\mathrm{PQR}$$ ...

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

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

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 ...

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 ...

$$P S$$ 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...

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...

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...

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...

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 $$\alpha$$...

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...

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

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...

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

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...

$$\mathrm{a}$$ 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...

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

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

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 ...

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...

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...

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...

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 $$\lambda^2=$$

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...

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

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

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

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...

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

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

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{...

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

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

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

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

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

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

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

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

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 $$\mathrm{4 h^2=}$$

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

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 :

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

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

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 $$\tan ^{-1}\left(\frac{1}{3}\right)$$,...