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AP EAMCET · Maths · Ellipse

The angle between the tangents drawn from a point \((-3,2)\) to the ellipse \(4 x^2+9 y^2-36=0\) is

  1. A \(45^{\circ}\)
  2. B \(\operatorname{Tan}^{-1}\left(\frac{2}{3}\right)\)
  3. C \(\operatorname{Tan}^{-1}\left(\frac{3}{2}\right)\)
  4. D \(90^{\circ}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(90^{\circ}\)

Step-by-step Solution

Detailed explanation

\(\text{Ellipse: } 4 x^2+9 y^2-36=0 \Rightarrow \frac{x^2}{9} + \frac{y^2}{4} = 1\). \(a^2=9, b^2=4\). \(\text{Equation of director circle: } x^2+y^2=a^2+b^2\). \(x^2+y^2=9+4=13\). \(\text{Check point } (-3,2) \text{ on director circle: } (-3)^2+2^2 = 9+4=13\).…