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 …

Question

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 AB subtends an angle equal to

Accepted Answer

$$\begin{aligned}
& 3 x-2 y+12=0 \
& 4 y=3 x^2 \
& \therefore 2(3 x+12)=3 x^2 \
& \Rightarrow x^2-2 x-8=0 \
& \Rightarrow x=-2,4 \
& \mathrm{~m}_{\mathrm{OA}}=-3 / 2, \mathrm{~m}_{\mathrm{OB}}=3 \
& \tan \theta=\left(\frac{\frac{-3}{2}-3}{1-\frac{9}{2}}\right)=\frac{9}{7} \
& \theta=\tan ^{-1}\left(\frac{9}{7}\right) \text { (angle will be acute) }
\end{aligned}$$

Solutions · 1