Q43 / 155 · WBJEE 2022 · Mathematics
A line passes through the point $(-1,1)$ and makes an angle $\sin ^{-1}\left(\frac{3}{5}\right)$ in the positive direction of $x$-axis. If this line meets the curve $x^2=4 y-9$ at $A$ and $B$, then $|A B|$ is equal to
- A$\frac{4}{5}$ unit
- Correct answerB$\frac{5}{4}$ unit
- C$\frac{3}{5}$ unit
- D$\frac{5}{3}$ unit
Solution
$4 y-3 x=7$ and $x^2=4 y-9$
On solving, $x^2-3 x+2=0 \Rightarrow x=1,2$ and $y=\frac{5}{2}, \frac{13}{4}$
$A\left(1, \frac{5}{2}\right)$ and $B\left(2, \frac{13}{4}\right)$
$$
|A B|=\frac{5}{4}
$$
Hence, the correct answer is option: 'B'.