The equation of an ellipse, whose vertices are $(2, -2), (2, 4)$ and eccentricity $\frac{1}{3}$, is
The equation of an ellipse, whose vertices are $(2, -2), (2, 4)$ and eccentricity $\frac{1}{3}$, is
- A
$\frac{{{{(x - 2)}^2}}}{9} + \frac{{{{(y - 1)}^2}}}{8} = 1$
- B
$\frac{{{{(x - 2)}^2}}}{8} + \frac{{{{(y - 1)}^2}}}{9} = 1$
- C
$\frac{{{{(x + 2)}^2}}}{8} + \frac{{{{(y + 1)}^2}}}{9} = 1$
- D
$\frac{{{{(x - 2)}^2}}}{9} + \frac{{{{(y + 1)}^2}}}{8} = 1$
Similar Questions
Consider two straight lines, each of which is tangent to both the circle $x ^2+ y ^2=\frac{1}{2}$ and the parabola $y^2=4 x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O (0,0)$ and whose semi-major axis is $OQ$. If the length of the minor axis of this ellipse is $\sqrt{2}$, then which of the following statement($s$) is (are) $TRUE$?
$(A)$ For the ellipse, the eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is $1$
$(B)$ For the ellipse, the eccentricity is $\frac{1}{2}$ and the length of the latus rectum is $\frac{1}{2}$
$(C)$ The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$ and $x=1$ is $\frac{1}{4 \sqrt{2}}(\pi-2)$
$(D)$ The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$ and $x=1$ is $\frac{1}{16}(\pi-2)$
Consider two straight lines, each of which is tangent to both the circle $x ^2+ y ^2=\frac{1}{2}$ and the parabola $y^2=4 x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O (0,0)$ and whose semi-major axis is $OQ$. If the length of the minor axis of this ellipse is $\sqrt{2}$, then which of the following statement($s$) is (are) $TRUE$?
$(A)$ For the ellipse, the eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is $1$
$(B)$ For the ellipse, the eccentricity is $\frac{1}{2}$ and the length of the latus rectum is $\frac{1}{2}$
$(C)$ The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$ and $x=1$ is $\frac{1}{4 \sqrt{2}}(\pi-2)$
$(D)$ The area of the region bounded by the ellipse between the lines $x=\frac{1}{\sqrt{2}}$ and $x=1$ is $\frac{1}{16}(\pi-2)$
- [IIT 2018]
The equation of ellipse whose distance between the foci is equal to $8$ and distance between the directrix is $18$, is
The equation of ellipse whose distance between the foci is equal to $8$ and distance between the directrix is $18$, is
If a tangent having slope of $ - \frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to .................. $\mathrm{sq. \, units}$ ($O$ is centre of the ellipse)
If a tangent having slope of $ - \frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{{32}} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to .................. $\mathrm{sq. \, units}$ ($O$ is centre of the ellipse)
An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is $2/3 $ then the eccentricity of the ellipse is :
An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is $2/3 $ then the eccentricity of the ellipse is :
If $\frac{{\sqrt 3 }}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ then its, eccentric angle $\theta $ is equal to: ................ $^o$
If $\frac{{\sqrt 3 }}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ then its, eccentric angle $\theta $ is equal to: ................ $^o$