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If the line $y=m x+c$ is a tangent to the parabola $y^2=4 a(x+a)$ then $m a+\frac{a}{m}$ is equal to
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The correct answer is:
$c$
Tangent at $y^2=4 a x$ is $y=m x+\frac{a}{m}$
Therefore, tangent at $y^2=4 a(x+a)$ is,
$y=m(x+a)+\frac{a}{m}$
or $y=m x+m a+\frac{a}{m} \Rightarrow m a+\frac{a}{m}=c$.
Therefore, tangent at $y^2=4 a(x+a)$ is,
$y=m(x+a)+\frac{a}{m}$
or $y=m x+m a+\frac{a}{m} \Rightarrow m a+\frac{a}{m}=c$.
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