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Point Form of Tangent: Hyperbola

If the equati...

Question

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

a + b = 2

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a (5 + b) = 4

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2 a = b

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a = 2 b

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Solution

The correct option is B $2 a = b$
Solution -
$y = a x^{2} + b$

$\frac{d y}{d x} = 2 a x$

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

$2 a x = 4$

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

This point satisfies $y = 4 x - 5$

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

$4 + a b = 8 - 5 a$

$a b + 5 a = 4$

$a (b + 5) = 4$

B is correct

Suggest Corrections

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