Question

The condition that the line  be a normal to the parabola  

y2 = 4ax is

Solution

Correct option is

p3 = 2ap2 + aq2

….. (1) is normal of y2 = 4ax. Its slope is . But equation of normal of parabola y2 = 4axis

y = mx – 2am – am3.

Comparing this with (1). q = – 2am – am3.

  

 p3 = 2ap2 + aq2.

 

SIMILAR QUESTIONS

Q1

If the straight line x + y = 1 touches the parabola y2 – y + x = 0, then the coordinates of the point of contact are

Q2

The angle of intersection between the curves y2 = 4x and x2 = 32y at point (16, 8) is

Q3

The pole of the line lx + mx + n = 0 with respect to the parabola y2 = 4ax is

Q4

Two tangent are drawn from the point (–2, –1) to the parabola y2 = 4x. if  is the angle between them, then 

Q5

The conic represented by the equation  is

Q6

If (4, 0) is the vertex and y-axis, the directrix of a parabola then its focus is

Q7

The straight line y = mx + c touches the parabola y2 = 4a(x + a) if

Q8

The focus of the parabola x2 – 2x – y + 2 = 0 is

Q9

If P1Q1 and P2Q2 are two focal chords of the parabola y2 = 4ax, then the chords P1P2 and Q1Q2 intersect on the

Q10

The equation of the normal to the hyperbola y2 = 4x, which passes through the point (3, 0), is