Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 …

Question

Let the latus ractum of the parabola y2
 = 4x be
the common chord to the circles C1
 and C2
each of them having radius 2$$\sqrt 5 $$. Then, the
distance between the centres of the circles C1
and C2
 is :

Accepted Answer

For parabola y2 = 4x,

Length of latus rectum = 4a = 4

C1C2 = 2(C1A)

C1A = $$\sqrt {{{(2\sqrt 5 )}^2} - {2^2}}  = 4$$

$$ \therefore $$ C1C2 = 2(4) = 8

Solutions · 1