The number of points outside the hyperbola x 2 16 - y 2 25 -1 from where two tangents can be drawn to the hyperbola is-are

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Director Circle

The number of...

Question

The number of points outside the hyperbola $\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1$ from where two $⊥$ tangents can be drawn to the hyperbola is/are

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Solution

The correct option is A $0$
Def: The director circle of a hyperbola is the locus of points from which $⊥$ tangent are drawn to the given hyperbolar. Equation of director circle of
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is given by $x^{2} + y^{2} = a^{2} - b^{2} = 16 - 25 = - 9$ which is impossible
$∴$ no point exist outside the hyperbola $\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1$

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The number of points outside the hyperbola x216+y225=1 from where two ⊥ tangents can be drawn to the hyperbola is/are

The correct option is A 0Def: The director circle of a hyperbola is the locus of points from which ⊥ tangent are drawn to the given hyperbolar. Equation of director circle ofx2a2+y2b2=1 is given by x2+y2=a2−b2=16−25=−9 which is impossible∴ no point exist outside the hyperbola x216+y225=1

The number of points outside the hyperbola $\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1$ from where two $⊥$ tangents can be drawn to the hyperbola is/are