Question

Tangents are drawn from the point (–8, 3) to the parabola

y² – 6y – 8x – 7 = 0. The angle between the tangents is

• A. 30⁰
• B. 90⁰
• C. 120⁰
• D. None of these

Answer 1

Answer: (C)

120⁰

Answer 2

y² – 6y – 8x – 7 = 0

y² – 6y + 9 = 8x + 7 + 9

(y – 3)² = 8(x + 2)

equation of Directrix

x + 2 = – 2

x + 4 = 0

tan q = $\frac{\sqrt{S_{1}}}{x_{1} + a}$ = $\frac{\sqrt{9 - 18 + 64 - 7}}{- 8 + 4}$

tan q = $\frac{4\sqrt{3}}{- 4}$

̃ tan q = –$\sqrt{3}$

̃ q =120⁰