# Straight Lines and Pair of Straight Lines · Mathematics · AP EAPCET

Start Practice## MCQ (Single Correct Answer)

AP EAPCET 2022 - 4th July Morning Shift

The least distance from origin to a point on the line $$y=x+3$$ which lies at a distance of 2 units from $$(0,3)$$ is

AP EAPCET 2022 - 4th July Morning Shift

Starting from the point $$A(-3,4)$$, a moving object touches $$2 x+y-7=0$$ at $$B$$ and reaches the point $$C(0,1)$$. If the object travels along the ...

AP EAPCET 2022 - 4th July Morning Shift

Suppose a triangle is formed by $$x+y=10$$ and the coordinate axes. Then, the number of points $$(x, y)$$ where $$x$$ and $$y$$ are natural numbers, l...

AP EAPCET 2022 - 4th July Morning Shift

If the lines represented by $$a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$$ intersect on the $$X$$-axis, which of the following is in general incorrect?...

AP EAPCET 2022 - 4th July Morning Shift

For $$\alpha \in\left[0, \frac{\pi}{2}\right]$$, the angle between the lines represented by $$[x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \...

AP EAPCET 2021 - 20th August Morning Shift

When the axes are rotated through an angle
45$$^\circ$$, the new coordinates of a point P are
(1, $$-$$1). The coordinates of P in the original
system...

AP EAPCET 2021 - 20th August Morning Shift

Find the equation of a straight line passing through $$(-5,6)$$ and cutting off equal intercepts on the coordinate axes.

AP EAPCET 2021 - 20th August Morning Shift

Line has slope $$m$$ and $$y$$-intercept 4 . The distance between the origin and the line is equal to

AP EAPCET 2021 - 20th August Morning Shift

The equation of the base of an equilateral triangle is $$x+y=2$$ and one vertex is $$(2,-1)$$, then the length of the side of the triangle is

AP EAPCET 2021 - 20th August Morning Shift

The equation of a straight line which passes through the point $$\left(a \cos ^3 \theta, a \sin ^3 \theta\right)$$ and perpendicular to $$(x \sec \the...

AP EAPCET 2021 - 20th August Morning Shift

The acute angle between lines $$6 x^2+11 x y-10 y^2=0$$ is

AP EAPCET 2021 - 20th August Morning Shift

If the lines, joining the origin to the points of intersection of the curve $$2 x^2-2 x y+3 y^2+2 x-y-1=0$$ and the line $$x+2 y=k$$, are at right ang...

AP EAPCET 2021 - 20th August Morning Shift

The equation of bisector of the angle between the lines represented by $$3 x^2-5 x y+4 y^2=0$$ is

AP EAPCET 2021 - 20th August Morning Shift

If the bisectors of the pair of lines $$x^2-2 m x y-y^2=0$$ is represented by $$x^2-2 n x y-y^2=0$$, then

AP EAPCET 2021 - 19th August Evening Shift

If $$A(4,7), B(-7,8)$$ and $$C(1,2)$$ are the vertices of $$\triangle A B C$$, then the equation of perpendicular bisector of the side $$A B$$ is...

AP EAPCET 2021 - 19th August Evening Shift

The ratio in which the straight line $$3 x+4 y=6$$ divides the join of the points $$(2,-1)$$ and $$(1,1)$$ is

AP EAPCET 2021 - 19th August Evening Shift

Find the equation of a line passing through the point $$(4,3)$$, which cuts a triangle of minimum area from the first quadrant.

AP EAPCET 2021 - 19th August Evening Shift

If the orthocenter of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y+1=0$$ and $$a x+b y-1=0$$ lies at origin, then $$\frac{1}{a}+\frac{1}{b}$$...

AP EAPCET 2021 - 19th August Evening Shift

The equation $$8 x^2-24 x y+18 y^2-6 x+9 y-5=0$$ represents a

AP EAPCET 2021 - 19th August Evening Shift

Find the angle between the pair of lines represented by the equation $$x^2+4 x y+y^2=0$$.

AP EAPCET 2021 - 19th August Evening Shift

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

AP EAPCET 2021 - 19th August Evening Shift

The angle between the lines represented by $$\cos \theta(\cos \theta+1) x^2-\left(2 \cos \theta+\sin ^2 \theta\right) x y+(1-\cos \theta) y^2=0$$ is...

AP EAPCET 2021 - 19th August Morning Shift

If the axes are rotated through an angle $$45 \Upsilon$$, the coordinates of the point $$(2 \sqrt{2},-3 \sqrt{2})$$ in the new system are

AP EAPCET 2021 - 19th August Morning Shift

the sum of the squares of the intercepts made the line $$5x-2y=10$$ on the coordinate axes equals

AP EAPCET 2021 - 19th August Morning Shift

For three consecutive odd integers $$a \cdot b$$ and $$c$$, if the variable line $$a x+b y+c=0$$ always passes through the point $$(\alpha, \beta)$$, ...

AP EAPCET 2021 - 19th August Morning Shift

If $$2x+3y+4=0$$ is the perpendicular bisector of the line segment joining the points A(1, 2) and B($$\alpha,\beta$$), then the value of $$13\alpha+13...

AP EAPCET 2021 - 19th August Morning Shift

The equation of the pair of straight lines perpendicular to the pair $$2 x^2+3 x y+2 y^2+10 x+5 y=0$$ and passing though the origin is

AP EAPCET 2021 - 19th August Morning Shift

If the centroid of the triangle formed by the lines $$2 y^2+5 x y-3 x^2=0$$ and $$x+y=k$$ is $$\left(\frac{1}{18}, \frac{11}{18}\right)$$, then the va...

AP EAPCET 2021 - 19th August Morning Shift

If $$m_1$$ and $$m_2,\left(m_1>m_2\right)$$ are the slopes of the lines represented by $$5 x^2-8 x y+3 y^2=0$$, then $$m_1: m_2$$ equals

AP EAPCET 2021 - 19th August Morning Shift

If the slope of one of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is the square of the other then, $$\left|\frac{a+b}{h}+\frac{8 h^2}{a b}\rig...