Question

Slope of common tangent to parabolas y2 = 4x and x2 = 8y is

Solution

Correct option is

Any tangent to y2 = 4x will be to the from . If this is a tangent to x2 = 8y, then roots of  must be real and equal so .

SIMILAR QUESTIONS

Q1

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

Q2

Find the locus of middle point of chord y2 = 4ax drawn through vertex.

Q3

Find the locus of the mid-point of the chords of the parabola y2 = 4ax which subtend a right angle at the vertex of the parabola.

Q4

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q5

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q6

Find the locus of a pint P which moves such that two of the three normal’s drawn from it to the parabola y2 = 4ax are mutually perpendicular.

Q7

If normal at the point (at2, 2at) in the parabola y2 = 4axintersects the parabola again at the (am2, 2am), then find the minimum value of m2.

Q8

The equation of circle touching the parabola y2 = 4x at the point  (1, –2) and passing through origin is

Q9

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

Q10

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is