Question

plz answer correctly.........
No stupid answers plz

Answer 1

Let the Equation of circle be :

x^2 + y^2 + 2gx + 2fy + c = 0.

Given that it cuts the circle x^2 + y^2 = 4 orthogonally.

⇒ 2(g * 0 + f * 0) = c - 4

⇒ c - 4 = 0

⇒ c = 4.

Given that it passes through the point(a,b).

⇒ a^2 + b^2 + 2ga + 2fb + 4 = 0.

Locus of center (-g,-f) is:

⇒ a^2 + b^2 - 2ax + 2by + 4 = 0

⇒ 2ax +2by = a^2 + b^2 + 4

(or)

2ax + 2by - (a^2 + b^2 + 4) = 0

Therefore:

The locus of its centre is : 2ax + 2by - (a^2 + b^2 + 4) = 0.

Hope it helps!