Question

If $y = 4x - 5$is a tangent to the curve $y^{2} = px^{3} + q$at (2,3) then :

• A. p = 2, q = -7
• B. p = -2, q = 7
• C. p = -2, q = -7
• D. p =2, q = 7

Answer 1

Answer: (A)

p = 2, q = -7

Answer 2

Given (2,3) lies on $y^{2} = px^{3} + q$ we get 9 = 8p + q……..(1)

Again $y^{2} = px^{3} + q$

⇒ $2y\frac{dy}{dx} = 3px^{2}$

⇒ $\frac{dy}{dx} = \frac{3px^{2}}{2y}$

⇒ $\left( \frac{dy}{dx} \right)_{(2,3)} = \frac{12p}{6} = 2p$

since $y = 4x - 5$is tangent to $y^{2} = px^{3} + q$ at $(2,3)$ therefore 2p = 4

$\left\lbrack \because\text{ Scope of line y } = \text{ 4x - 5 is 4} \right\rbrack$⇒ p -2. Putting p=2 in equation (1), we get q= -7

Hence p = 2, q = -7.