JEE Main 2024 (Online) 4th April Morning Shift | Parabola Question 9 | Mathematics

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JEE Main 2024 (Online) 4th April Morning Shift

Numerical

+4

-1

Let the length of the focal chord PQ of the parabola $$y^2=12 x$$ be 15 units. If the distance of $$\mathrm{PQ}$$ from the origin is $$\mathrm{p}$$, then $$10 \mathrm{p}^2$$ is equal to __________.

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2

JEE Main 2024 (Online) 1st February Morning Shift

Numerical

+4

-1

Let the line $\mathrm{L}: \sqrt{2} x+y=\alpha$ pass through the point of the intersection $\mathrm{P}$ (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2 y$. Let the line $\mathrm{L}$ touch two circles $\mathrm{C}_1$ and $\mathrm{C}_2$ of equal radius $2 \sqrt{3}$. If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the $y$-axis, then the square of the area of the triangle $\mathrm{PQ}_1 \mathrm{Q}_2$ is equal to ___________.

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3

JEE Main 2024 (Online) 29th January Evening Shift

Numerical

+4

-1

Let $$P(\alpha, \beta)$$ be a point on the parabola $$y^2=4 x$$. If $$P$$ also lies on the chord of the parabola $$x^2=8 y$$ whose mid point is $$\left(1, \frac{5}{4}\right)$$, then $$(\alpha-28)(\beta-8)$$ is equal to _________.

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4

JEE Main 2023 (Online) 11th April Evening Shift

Numerical

+4

-1

Out of Syllabus

Let the tangent to the parabola $$\mathrm{y}^{2}=12 \mathrm{x}$$ at the point $$(3, \alpha)$$ be perpendicular to the line $$2 x+2 y=3$$. Then the square of distance of the point $$(6,-4)$$ from the normal to the hyperbola $$\alpha^{2} x^{2}-9 y^{2}=9 \alpha^{2}$$ at its point $$(\alpha-1, \alpha+2)$$ is equal to _________.

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