Sponsor Area
Conic Section
Question
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = p2 orthogonally, then the equation of the locus of its centre is
-
x2 + y2 – 3ax – 4by + (a2 + b2 – p2 ) = 0
-
2ax + 2by – (a2 – b2 + p2 ) = 0
-
x2 + y2 – 2ax – 3by + (a2 – b2 – p2 ) = 0
-
2ax + 2by – (a2 + b2 + p2 ) = 0
Solution
D.
2ax + 2by – (a2 + b2 + p2 ) = 0
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 pass through (a, b) ⇒ a2 + b2 - 2αa - 2βb + p2 = 0
Locus ∴ 2ax + 2by – (a2 + b2 + p2 ) = 0.
Sponsor Area
Mock Test Series
Mock Test Series