MAH CET MCA Conic Section Previous Year Questions (PYQs)
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The number of values of $C$ such that the straight line $y = 4x + C$ touches the curve $x^2 + 4y^2 = 4$ is
1
2
3
4
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.
Line intersect on the hyperbola at points $(-2,-6)$ and $(4,2)$, and their asymptotes are $(1,-2)$. Then the centre of the hyperbola is
1
2
3
4
Solution
Midpoint of intersecting points $(-2,-6)$ and $(4,2)$ gives centre:
$\left(\dfrac{-2+4}{2}, \dfrac{-6+2}{2}\right) = (1,-2)$.
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