Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (B)

$1$

Equation of asymptotes is $y-y_1=\pm \frac{a}{b}(x-x_1)$ where ($x_1,y_1$) is focus
$y-2=\pm \frac{2}{3}(x-1)$
$⟹3y-2x=4$ and $3y+2x=8$
As given line is parallel to one of the asymptotes, it will cut at one point only