Question

If 2x + y + 1 = 0 is a tangent to the parabola y² = 8x, the point of contact is

• A. (1/2, –2)
• B. (–2/3, 1/3)
• C. (2, –4)
• D. None

Answer 1

Answer: (A)

(1/2, –2)

Answer 2

2x + y + 1 = 0

tangent m = – 2

y² = 8x

2y $\frac{dy}{dx}$ = 8

̃ $\frac{dy}{dx}$ = $\frac{4}{y}$ = –2 ̃ y = –2

4 = 8x ̃ x = 1/2

Hence $\left( \frac{1}{2}, - 2 \right)$