Question

If (a, b), (c, d) are points on the curve 9y² = x³ where the normal makes equal intercepts on the axes, then the value of a + b + c + d is ______.

Options

• 0

• 8

• 27

• 64

Answer 1

If (a, b), (c, d) are points on the curve 9y² = x³ where the normal makes equal intercepts on the axes, then the value of a + b + c + d is 8.

Explanation:

Let `(t^2, t^3/3)` is any point on 9y² = x³

Normal makes equal intercepts

⇒ Slope = ±1

∴ `(dy)/(dx) = t^2/(2t)` = ±1

⇒ t = ±2

∴ The Points are (a, b) = `(4, 8/3),(4, (-8)/3)`

∴ Required sum = 8