MathematicsThe number of tangents to x225–y29= 1 through (5, 0) is _____

The number of tangents to $\frac{x^{2}}{25} - \frac{y^{2}}{9} = 1$ through (5, 0) is $_____$

Solution:

$let S \equiv \frac{x^{2}}{25} - \frac{y^{2}}{9} - 1 Now S (5, 0) = \frac{25}{25} - 0 - 1 = 0 ∴ Given point lies on t h e hyperbola . ∴ Number of tangents = 1$

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