Question

AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

• A. a
• B. 2a
• C. 4a
• D. 8a

Answer 1

Answer: (C)

4a

Answer 2

Let B be (at2, 2at)

Slope of AB =$\frac{2}{t}$.

Equation of BC is y – 2at = – $\frac{1}{2}$ (x – at2).

This meets y = 0 at C whose x-coordinate = 4a + at2

D = (at2, 0)

\ DC = 4a + at2 – at2 = 4a.