If the equation of the tangent to the curve `y^2=a x^3+b` at point `(2,3)i sy=4x-5` , then find the values of `a` `"and"` `b` .

Options

A. 3,-5
B. 6,-5
C. 6,15
D. 6,-15

Answer

D

Explanation

Given , `y^(2) = ax^(2) + b^(2) " " … (i)`
`therefore 2y""(dy)/(dx) = 2ax`
`implies (dy)/(dx) = (ax)/(y)`
`therefore ` Slope at (2,3) = `((dy)/(dx))_((2,3)) = (2a)/(3)`
But slope of given tangent is m = 4
`therefore (2a)/(3) = 4 implies a = 6`
Since , point (2, 3) lies on the curve so , it satisfies the equation of the curve
`therefore (3)^(2) = 6(2)^(2) + b`
`implies b = -15`