JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the points of intersection of the ellipses \( x^{2}+2y^{2}-6x-12y+23=0 \) and \( 4x^{2}+2y^{2}-20x-12y+35=0 \) lie on a circle of radius \( r \) and centre \( (a, b) \), then the value of \( ab+18r^{2} \) is:
- A 53
- B 51
- C 52
- D 55
Answer & Solution
Correct Answer
(D) 55
Step-by-step Solution
Detailed explanation
By family of curve equation of circle will be \(\Rightarrow S _1+\lambda S _2=0\) \(\Rightarrow\left(x^2+2 y^2-6 x-12 y+23\right)\) \(+\lambda\left(4 x^2+2 y^2-20 x-12 y+35\right)=0\) ⇒ for circle coeff of \(x^2=\operatorname{coeff}\). of \(y^2\)…
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