Two straight lines are perpendicular to each other. One of them touches the parabola `y^2=4a(x+a)` and the other touches `y^2=4b(x+b)` . Their point of intersection lies on the line. (a)`x-a+b=0` (b) `x+a-b=0` (c)`x+a+b=0` (d) `x-a-b=0`

Prove that the line x/l+y/m=1 touches the parabola y^2=4a(x+b) , if m^2(l+b)+al^2=0 .

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

The planes x=0 and y=0 (A) are parallel (B) are perpendicular to each other (C) interesect in z-axis (D) none of these

Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x+y+4=0 . If A and B are the points of intersection of C with the line y=-5 , then the distance between A and B is

Prove that the line x/a + y/b =1 and x/b - y/a =1 are perpendicular to each other.

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

Find the equation of the line passing through the point of intersection of the lines x+5y+7=0 and 3x+2y-5=0 (b) perpendicular to the line 7x + 2y - 5 = 0

The point on the line x-y+ 2= 0 from which the tangent to the parabola y^2= 8x is perpendicular to the given line is (a, b) , then the line ax + by+c=0 is

The two lines represented by 3a x^2+5x y+(a^2-2)y^2=0 are perpendicular to each other for (a) two values of a (b) a (c) for one value of a (d) for no values of a