Paragraph: Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$…

Paragraph: Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.Question: The coordinates of $A$ and $B$ are
  1. $(3,0)$ and $(0,2)$
  2. $\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$
  3. $\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $(0,2)$
  4. $(3,0)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$

Solution

$ \text { Figure is self explanatory } $

Asked in: JEE Advanced 2010 (Paper 2)

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