Dear student,
Please find the attached solution to your problem below.
Let the centre be (α, β)
∵It cut the circle x2 + y2 = p2 orthogonally
2(-α) × 0 + 2(-β) × 0 = c1 – p2
c1 = p2
Let equation of circle is x2 + y2 - 2αx - 2βy + p2 = 0
It passes through (a, b) ⇒ a2+ b2- 2αa - 2βb + p2 = 0
Locus ∴ 2ax + 2by – (a2 + b2 + p2) = 0.
Thanks and regards,
Kushagra
