WBJEE · Maths · Straight Lines
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
- B \(\frac{5}{4}\) unit
- C \(\frac{3}{5}\) unit
- D \(\frac{5}{3}\) unit
Answer & Solution
Correct Answer
(B) \(\frac{5}{4}\) unit
Step-by-step Solution
Detailed explanation
\(4 y-3 x=7\) 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 \(B\left(2, \frac{13}{4}\right)\) \[ |A B|=\frac{5}{4} \]
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