1

JEE Main 2023 (Online) 15th April Morning Shift

Numerical

+4

-1

Let an ellipse with centre $(1,0)$ and latus rectum of length $\frac{1}{2}$ have its major axis along $\mathrm{x}$-axis. If its minor axis subtends an angle $60^{\circ}$ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to ____________.

Your input ____

2

JEE Main 2023 (Online) 1st February Evening Shift

Numerical

+4

-1

The line $$x=8$$ is the directrix of the ellipse $$\mathrm{E}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ with the corresponding focus $$(2,0)$$. If the tangent to $$\mathrm{E}$$ at the point $$\mathrm{P}$$ in the first quadrant passes through the point $$(0,4\sqrt3)$$ and intersects the $$x$$-axis at $$\mathrm{Q}$$, then $$(3\mathrm{PQ})^{2}$$ is equal to ____________.

Your input ____

3

JEE Main 2023 (Online) 24th January Morning Shift

Numerical

+4

-1

Let C be the largest circle centred at (2, 0) and inscribed in the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$. If (1, $$\alpha$$) lies on C, then 10 $$\alpha^2$$ is equal to ____________

Your input ____

4

JEE Main 2023 (Online) 24th January Morning Shift

Numerical

+4

-1

Let a tangent to the curve $$9{x^2} + 16{y^2} = 144$$ intersect the coordinate axes at the points A and B. Then, the minimum length of the line segment AB is ________

Your input ____

Questions Asked from Ellipse (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2023 (Online) 15th April Morning Shift (1)
JEE Main 2023 (Online) 1st February Evening Shift (1)
JEE Main 2023 (Online) 24th January Morning Shift (2)
JEE Main 2022 (Online) 28th July Evening Shift (1)
JEE Main 2022 (Online) 27th July Morning Shift (1)
JEE Main 2022 (Online) 24th June Morning Shift (1)
JEE Main 2021 (Online) 27th August Morning Shift (1)
JEE Main 2021 (Online) 27th July Evening Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (1)

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