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Slope Form of Tangent

If y=mx+c tou...

Question

If $y = m x + c$ touches the parabola $y^{2} = 4 a (x + a)$ , then

A

c = \frac{a}{m}

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B

c = a m + \frac{a}{m}

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C

c = a + \frac{a}{m}

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D

none of these

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Solution

The correct option is B $c = a m + \frac{a}{m}$
Equation of tangent to given parabola having slope $m$ is
$y = m (x + a) + \frac{a}{m}$
or $y = m x + a m + \frac{a}{m} \dots (i)$
Comparing equation $(i)$ with $y = m x + c,$ we have
$c = a m + \frac{a}{m}$

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Slope Form of Tangent

Standard XIII Mathematics

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