JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If the line \(3 x-2 y+12=0\) intersects the parabola \(4 y=3 x^2\) at the points \(A\) and \(B\), then at the vertex of the parabola, the line segment \(A B\) subtends an angle equal to
- A \(\tan ^{-1}\left(\frac{4}{5}\right)\)
- B \(\tan ^{-1}\left(\frac{9}{7}\right)\)
- C \(\tan ^{-1}\left(\frac{11}{9}\right)\)
- D \(\frac{\pi}{2}-\tan ^{-1}\left(\frac{3}{2}\right)\)
Answer & Solution
Correct Answer
(B) \(\tan ^{-1}\left(\frac{9}{7}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 3 x-2 y+12=0 \\ & 4 y=3 x^2 \\ & \therefore 2(3 x+12)=3 x^2 \\ & \Rightarrow x^2-2 x-8=0 \\ & \Rightarrow x=-2,4 \\ & \mathrm{~m}_{\mathrm{OA}}=-3 / 2, \mathrm{~m}_{\mathrm{OB}}=3 \\ & \tan \theta=\left(\frac{\frac{-3}{2}-3}{1-\frac{9}{2}}\right)=\frac{9}{7} \\…
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