How many real tangents can be drawn to ellipse 5x^2 + 9y^2 = 32 from point (2,3)

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10-2. Parabola, Ellipse, Hyperbola

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How many real tangents can be drawn to the ellipse $5x^2 + 9y^2 = 32$ from the point $(2,3)$

A

$2$

B

$1$

C

$0$

D

$3$

Solution

Let $S \equiv 5{x^2} + 9{y^2} – 32$

$\mathrm{Now}$ $S(2,3) \equiv 20+81-32>0$

$\therefore $ Point $(2,3)$ lies outside ellipse.

Thus, two tangents can be drawn.

Standard 11

Mathematics

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