The perpendicular tangents drawn to the hyperbola nbsp-x225-y216-1 intersect on the curve nbsp-x2-y2-9FalseTrue

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Director Circle: Hyperbola

The perpendic...

Question

The perpendicular tangents drawn to the hyperbola
$\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$
intersect on the curve $x^{2} + y^{2} = 9$

False

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True

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Solution

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\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1

x^{2} + y^{2} = 9

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

e > \sqrt{2}

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

x^{2} + y^{2} = a^{2} - b^{2}

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

c^{2}

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

x^{2} + y^{2} = a^{2} - b^{2}

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