Question

Parabolas y2=4a(xc1) and x2=4a(yc2), where c1 and c2 are variable, are such that they touch each other. Locus of their point of contact is

Answer 1

parabolas y^2 = 4a(x-c1) and x^2=4a(y-c2),where c1 and c2 are variables,are such that they touch each other.Locus of their point of contact is ...


solve : equation of parabolas are : y² = 4a(x - c1) and x² = 4a(y - c2) where c1 and c2 are variables.

here both the given curves touch each other at two points. at point of contact is (x, y) . then slope of both curves at (x,y) are same.

y² = 4a(x - c1)
differentiate with respect to x,
2yy' = 4a......(1)

x² = 4a(y - c2)
differentiate with respect to x,
2x = 4ay' ........(2)

solve equations (1) and (2),
xy = 4a²

hence, locus of point of contact is xy = 4a²