JEE Main2005MathematicsCircleActual
If a circle passes through the point (a, b) and cuts the circle x^2+y^2=p^2 orthogonally, then the equation of the locus of its centre is
Options
- Ax^2+y^2-3 a x-4 b y+ (a^2+b^2-p^2 )=0
- B2 a x+2 b y- (a^2-b^2+p^2 )=0
- Cx^2+y^2-2 a x-3 b y+ (a^2-b^2-p^2 )=0
- D2 a x+2 b y- (a^2+b^2+p^2 )=0
Correct answer
D. 2 a x+2 b y- (a^2+b^2+p^2 )=0
Step-by-step solution
Let the centre be ( , ) It cut the circle x ^2+ y ^2= p ^2 orthogonally 2(- ) 0+2(- ) 0=c₁-p^2 c ₁= p ^2 Let equation of circle is x^2+y^2-2 x-2 y+p^2=0 It pass through (a, b) a^2+b^2-2 a-2 b+p^2=0 Locus 2 a x+2 b y- (a^2+b^2+p^2 )=0