Question

If y = 4x – 5 is a tangent to the curve y² = px³ + q at (2, 3), find the value of (p – q – 4).

Answer 1

Given curve is y² = px³ + q

Hence, the equation of the tangent at (2, 3) is

y – 3 = 2p(x – 2)

which is identical with y = 4x – 5

Thus, 2p = 4 ⇒ p = 2

Since the point (2, 3) lies on the curve, so

8p + q = 9

⇒ 16 + q = 9

⇒ q = 9 – 16 = –7

Hence, the value of (p – q – 4)

= 2 + 7 – 4

= 9 – 4 = 5.