NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If y = 4 x - 5 is tangent to the curve y 2 = p x 3 + q at ( 2 , 3 ) then ( p , q ) is

Options

A( 2 , 7 )
B( - 2 , 7 )
C( - 2 , - 7 )
D( 2 , - 7 )

Correct answer

D. ( 2 , - 7 )

Step-by-step solution

Curve is y 2 = p x 3 + q ∴ 2 y d y d x = 3 p x 2 ⇒ d y d x ( 2,3 ) = 3 p . 4 2.3 ⇒ 4 = 2 p ⇒ p = 2 Also, curve is passing through ( 2 , 3 ) ∴ 9 = 8 p + q ⇒ q = - 7 ∴ p , q is 2 , - 7

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