JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Ellipse

More JEE Main questions on Ellipse

1. In the line $\alpha x+4y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3x^2+4y^2=1$ at the point P in the first quadrant, then one of the focal distances of P is :
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2. Let $S$ and $S^{\prime }$ be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $\mathrm{P}(\alpha ,\beta )$ be a point on the ellipse in the first quadrant. If …
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3. Let the line $y-x=1$ intersect the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :
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4. If the points of intersection of the ellipses $x^2+2y^2-6x-12y+23=0$ and $4x^2+2y^2-20x-12y+35=0$ lie on a circle of radius r and centre $(\mathrm{a},\mathrm{b})$, then the value of $\mathrm{ab}+18{\mathrm{r}}^2$ is
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5. Let each of the two ellipses ${\mathrm{E}}_1:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1,(\mathrm{a}>\mathrm{b})$ and ${\mathrm{E}}_2:\frac{{\mathrm{x}}^2}{{\mathrm{A}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{B}}^2}=1,(\mathrm{A}<\mathrm{B})$ …
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6. Let the length of the latus rectum of an ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1,(\mathrm{a}>\mathrm{b})$, be 30. If its eccentricity is the maximum value of the function $f(t)=-\frac{3}{4}+2t-t^2$, then …
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