Question

If the line 2x + 3y = 1 touch the parabola y2 = 4ax at the pointP. Find the focal distance of the point P.

Solution

Correct option is

Let point P be (at2, 2at). Then tangent at point P will be

            ty = x + at2.

Comparing with given the line 2x + 3y = 1.

We get 

So, focal distance of point P is .

SIMILAR QUESTIONS

Q1

The points on the parabola y2 = 36x whose ordinate is three times the abscissa are

Q2

The points on the parabola y2 = 12x whose focal distance is 4, are

Q3

Axis of the parabola x2 – 4x – 3+ 10 = 0 is  

Q4

The equation of the latus rectum of the parabola x2 + 4x + 2= 0 is 

Q5

x – 2 = t2y = 2t are the parameter equations of the parabola 

Q6

The equation  represents a parabola if  is

Q7

t1’ and ‘t2’ are two points on the parabola y2 = 4x. If the chord joining them is a normal to the parabola at ‘t1’ then

Q8

The vertex of the parabola y2 = 8x is at the center of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is

Q9

Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.

Q10

Find the angle between the tangents of the parabola y2 = 8x, which are drawn from the point (2, 5).