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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
MathematicsEllipseJEE AdvancedJEE Advanced 2010 (Paper 2)
Options:
  • A
    $(3,0)$ and $(0,2)$
  • B
    $\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$
  • C
    $\left(-\frac{8}{5}, \frac{2 \sqrt{161}}{15}\right)$ and $(0,2)$
  • D
    $(3,0)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$
Solution:
1022 Upvotes Verified Answer
The correct answer is:
$(3,0)$ and $\left(-\frac{9}{5}, \frac{8}{5}\right)$
$$
\text { Figure is self explanatory }
$$


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