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MAH CET MCA Previous Year Questions (PYQs)

MAH CET MCA Conic Section PYQ

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





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

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.
MAH CET MCA PYQ
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





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MAH CET MCA Previous Year PYQ MAH CET MCA MAH MCA CET 2023 PYQ

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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