Question

The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y2 = 8x  is

Solution

Correct option is

x2 + y2 – 10x = 0

 

y2 = 8x = 4ax, say.

Then a = 2. Ends of latus rectum are

     A(a, 2a), B(a,  –2a)   A(2, 4), B(2, –4).

Also vertex is V(0, 0). Any circle through V is

     x2 + y2 + 2gx +2fy = 0                      …. (1)

putting A and in (1),

     5a2 + 2ag + 4fa = 0                          …. (2)

     5a2 + 2ag – 4fa = 0                           …. (3)

(2), (3)  8fa = 0   f = 0

(2), (4)  5a2 + 2ag = 0 

Putting (4) and (6) in (1), x2 + y2 – 5ax = 0. Here

 x2 + y2 – 10x = 0

SIMILAR QUESTIONS

Q1

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Q2

The equation of common tangent to the curves y2 = 8x and xy = –1 is

Q3

From the point (–1, 2) tangent lines are drawn to the parabola y2 = 4x, then the equation of chord of contact is

Q4

For the above problem, the area of triangle formed by chord of contact and the tangents is given by

Q5

A point moves on the parabola y2 = 4ax. Its distance from the focus is minimum for the following value(s) of x.

Q6

The line x – y + 2 = 0 touches the parabola y2 = 8x at the point

Q7

If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is

Q8

The point on the parabola y2 = 8x at which the normal is inclined at 600 to the x-axis has the coordinates

Q9

The length of the latus rectum of the parabola 9x2 – 6x + 36y + 19 = 0 is

Q10

If the parabola y2 = 4ax passes through the pint (1, –2), then the tangent at this point is