The number of...

Question

The number of real points at which line $3 y - 2 x = 14$ cuts hyperbola $\frac{(x - 1)^{2}}{9} - \frac{(y - 2)^{2}}{4} = 5$ is

0

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Solution

The correct option is D $1$
Equation of asymptotes is $y - y_{1} = \pm \frac{a}{b} (x - x_{1})$ where ( $x_{1}, y_{1}$ ) is focus
$y - 2 = \pm \frac{2}{3} (x - 1)$
$⟹ 3 y - 2 x = 4$ and $3 y + 2 x = 8$
As given line is parallel to one of the asymptotes, it will cut at one point only

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