AP EAMCET · Maths · Ellipse
The square of the slope of a common tangent drawn to the circle \(4 x^2+4 y^2=25\) and the ellipse \(4 x^2+9 y^2=36\) is
- A 1
- B \(\frac{9}{11}\)
- C \(\frac{2}{3}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\frac{9}{11}\)
Step-by-step Solution
Detailed explanation
Circle: \(x^2+y^2 = \frac{25}{4}\) so \(r = \frac{5}{2}\). Ellipse: \(\frac{x^2}{9} + \frac{y^2}{4} = 1\) so \(a^2=9, b^2=4\). Tangent to circle: \(y = mx \pm r \sqrt{1+m^2} \Rightarrow y = mx \pm \frac{5}{2} \sqrt{1+m^2}\). Tangent to ellipse:…
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