Question

If  and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then

   

Solution

Correct option is

d2 + (2b + 3c)2 = 0

The two parabolas meet at (0, 0) and (4a, 4a). Putting in the given line, we have d = 0 and 2ba + 3ac = 0  2b + 3c = 0.

SIMILAR QUESTIONS

Q1

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Q2

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Q3

Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.

Q4

The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is  

Q5

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Q6

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

Q7

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are

Q8

The curve described parametrically by x = t2 + t + 1, y = t2 – + 1 represents.

Q9

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

Q10

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid-point of PQ is