Question

If line PQ whose equation is y = 2x + k is a normal to the parabola whose vertex is (–2, 3) and axis parallel to x- axis with latus rectum equal to 2 then the value of k is-

• A. $\frac{58}{8}$
• B. $\frac{50}{8}$
• C. 1
• D. –1

Answer 1

Answer: (C)

1

Answer 2

4a = 2 ̃ a = $\frac{1}{2}$ Vertex º (–2, 3)

So parabola º (y – 3)² = 2 (x + 2)

Equation of normal to parabola

(y – 3) = m(x + 2) – m –$\frac{1}{2}$m³

̃ y = mx + m + 3 –$\frac{1}{2}$m³

also given y = 2x + k

m = 2 and k = m + 3 –$\frac{1}{2}$m³

k = 2 + 3 –$\frac{1}{2}$ (2)³ ̃ k = 5 – 4 = 1