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Previous Year Question (PYQs)

The number of values of $C$ such that the straight line $y = 4x + C$ touches the curve $x^2 + 4y^2 = 4$ is




Solution

Substitute $y = 4x + C$ in $x^2 + 4y^2 = 4$. To touch, discriminant $= 0$. After solving, $C = \pm \dfrac{2}{\sqrt{17}}$. Hence, there are $2$ possible values.

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