How may real tangents can be drawn from the point (5,3) to the hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1 ?$

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Solution

Given point P(5,3)

we have,Hyperbola $s = \frac{x^{2}}{25} - \frac{y^{2}}{9} - 1$

$∵ s_{1} = \frac{25}{25} - \frac{9}{9} - 1 = - 1 < 0$

$\Rightarrow p o i n t p \equiv (5, 3)$ lies outside the hyperbola.

$∴$ two tangents can be drawn from the point $p \equiv (5, 3)$

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How may real tangents can be drawn from the point (5,3) to the hyperbola x225−y29=1?

Given point P(5,3) we have,Hyperbola s=x225−y29−1 ∵s1=2525−99−1=−1<0 ⇒point p≡(5,3) lies outside the hyperbola. ∴ two tangents can be drawn from the point p≡(5,3)

How may real tangents can be drawn from the point (5,3) to the hyperbola $\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1 ?$

Given point P(5,3)

we have,Hyperbola $s = \frac{x^{2}}{25} - \frac{y^{2}}{9} - 1$

$∵ s_{1} = \frac{25}{25} - \frac{9}{9} - 1 = - 1 < 0$

$\Rightarrow p o i n t p \equiv (5, 3)$ lies outside the hyperbola.

$∴$ two tangents can be drawn from the point $p \equiv (5, 3)$