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  4. The equation of common tangent to the curves y2=20 x and (x2/25)+(y2/120)=1 having positive gradient is

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Q. The equation of common tangent to the curves $y^2=20 x$ and $\frac{x^2}{25}+\frac{y^2}{120}=1$ having positive gradient is

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Solution:

$y = mx +\frac{5}{ m }( m >0) $ ....(1)
$\therefore \frac{25}{ m ^2}=25 m ^2+120 \text { (using condition of tangency) } \Rightarrow m =\frac{1}{\sqrt{5}}$