AP EAMCET · Maths · Ellipse
If a tangent of slope 2 to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) touches the circle \(x^2+y^2=4\), then maximum value of \(a b\) is
- A 4
- B 12
- C 5
- D 7
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
Given the ellipse, \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) Since, tangent to the given ellipse with slope \(m=2\) is given as \(y=m x \pm \sqrt{a^2 m^2+b^2} \Rightarrow y=2 x \pm \sqrt{4 a^2+b^2}\) \(\because\) it touches the circle \(x^2+y^2=4\) So,…
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