If the chord of contact of tangents from a point P to the parabola y 2 = 4ax, touches the parabola x 2 = 4by, then the locus of P is a/an -
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Let P(h, k) be a point. Then the chord of contact of tangents from P to y 2 = 4ax is
ky = 2a (x + h)
This touches the parabola x 2 = 4by. So, it should be of the form
x = my + 
… (2)
Equation (1) can be re-written as
x = 
y – h … (3)
Since Equation (2) and (3) represent the same line.
∴ m = 
and 
= –h
Eliminating m from these two equations, we get
2ab = –hk
Hence, the locus of P(h, k) is
xy = –2ab, which is a hyperbola.
Hence is the correct answer.
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