Question

If the equation of the tangent to the curve $y=a{x}^2+b$ is $y=4x-5$, then

• A. $a+b=2$
• B. $a(5+b)=4$
• C. $2a=b$
• D. $a=2b$

Answer 1

Answer: (C)

$2a=b$

Solution -

$y=a{x}^2+b$

$\frac{dy}{dx}=2ax$

For line $=4x-5$ to be a tangent

$2ax=4$

$x=\frac{2}{a}$ $y=\frac{4}{a}+6=\frac{4+ab}{a}$

This point satisfies $y=4x-5$

$\frac{4+ab}{a}=\frac{8}{a}-5$

$4+ab=8-5a$

$ab+5a=4$

$a(b+5)=4$

B is correct