Question

The angle subtended by the chord 4y = 3x - 48 at the vertex of the parabola y²=64x is θ. Then tanθ =

• A. 20/9
• B. 10/9
• C. 5/9
• D. 5/2

Answer 1

Answer: (A)

20/9

Answer 2

Let the given line intersect the parabola at P and Q. Then the combined equation of the pair of lines $\overset{\leftrightarrow}{OP}\mspace{6mu} and\mspace{6mu}\overset{\leftrightarrow}{OQ}$ is obtained by homogesing the curve by the help of line.

∴ The combined equation of $\overset{\leftrightarrow}{OP}\mspace{6mu} and\mspace{6mu}\overset{\leftrightarrow}{OQ}$ is given by

y² – 64x $\left( \frac{3x - 4y}{48} \right)$ = 0.

⇒ 12x² – 3y² – 16xy = 0

∴ tanθ = $\frac{2\sqrt{h^{2} - ab}}{a + b} = \frac{20}{9}$