JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the radius of the largest circle with centre \((2,0)\) inscribed in the ellipse \(x^2+4 y^2=36\) is \(r\), then \(12 r^2\) is equal to
- A \(72\)
- B \(115\)
- C \(92\)
- D \(69\)
Answer & Solution
Correct Answer
(C) \(92\)
Step-by-step Solution
Detailed explanation
\((x-2)^2+y^2=r^2\) Solving with ellipse, we get \((x-2)^2+\frac{36-x^2}{4}=r^2\) \(3 x^2-16 x+52-4 r^2=0\) \(D=0 \Rightarrow 4 r^2=\frac{92}{3}\)
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