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  4. The number of values of c such that the straight line y=4x+c touches the curve (x2/4)+y2=1 , is

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Q. The number of values of $ c $ such that the straight line $ y=4x+c $ touches the curve $ \frac{x^{2}}{4}+y^{2}=1 $ , is

UPSEEUPSEE 2008

Solution:

For ellipse, condition of tangency is
$ c^{2}=a^{2} m^{2}+b^{2}$
$\Rightarrow c^{2} =4 \times 4^{2}+1=65$
$\Rightarrow c=\pm \sqrt{65}$