## Question

### Solution

Correct option is

x = 0

y2 = 4ax              … (1)

Its focus is S(a, 0). Any point on (1) is P (t12, 2t1).

Let M(x, y) be mid-point of chord PS, then  … (2) … (3)

Eliminating t between (2) and (3). Take Its directrix is X = –A .

#### SIMILAR QUESTIONS

Q1

Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents

Q2

The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.

Q3

The tangent at any point P of the hyperbola makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then

Q4

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y2 = 8x, is

Q5

The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is

Q6

The length of the subnormal to the parabola y2 = 4ax at any point is equal to

Q7

The slope of the normal at the point (at2, 2at) of parabola y2 = 4ax  is

Q8

Equation of locus of a point whose distance from point (a, 0) is equal to its distance from y-axis is

Q9

Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is

Q10

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