Question

Parabola `y^2=4a(x-c_1) and x^2=4a(y-c_2)` where `c_1 and c_2` are variables, touch each other. Locus of their point of contact is
A. `xy=2a^(2)`
B. `xy=4a^(2)`
C. `xy=a^(2)`
D. none of these

Answer 1

Correct Answer - B
(2) Let P(x,y) be the point of contact. At P, both of them must have the same slope. We have
`2y(dy)/(dx)=4a,2x=4a(dy)/(dx)`
Eliminating `dy//dx`, we get `xy=4a^(2)`.