Major Axis of Ellipse

Q. If the focal distance of an end of minor axis of any { ellipse, (whose axes along the x and y axes { respectively is k and the distance between the foci { is 2h . Then the equation of the ellipse is

Q.

Find the equation for the ellipse that satisfies the given conditions,
Ends fo major axis $(\pm 3,0)$ ends of minor axis $(0,\pm 2)$

Q. A circle and an ellipse have centres at $(0,0)$ and the circle passes through foci $F_1$ and $F_2$ of the ellipse, such that the two curves intersect at four points. Let $P$ be any one of their points of intersection. If the length of major axis of the ellipse is $17$ and area of the triangle $P{F}_1{F}_2$ is $30$, then distance between foci is

1. $11$
2. $12$
3. $13$
4. $15$

Q.

If the axes of the ellipse are coordinate axes and A and B are the ends of major axis and minor axis respectively.If the area of $△$OAB is 16 sq units, e = $\frac{\sqrt{3}}{2}$ then the equation of the ellipse is

1. $\frac{x^2}{32}+\frac{y^2}{8}$=1

2. $\frac{x^2}{64}+\frac{y^2}{16}$=1

3. $\frac{x^2}{64}+\frac{y^2}{8}$=1

4. $\frac{x^2}{64}+\frac{y^2}{32}$=1

Q. An equilateral triangle $SAB$ is inscribed in the parabola $y^2=4ax$ having its focus at $S$. If chord $AB$ lies towards the left of $S,$ then side length of this triangle is

1. $2a(2-\sqrt{3})$
2. $4a(2-\sqrt{3})$
3. $a(2-\sqrt{3})$
4. $8a(2-\sqrt{3})$

Q. The length of the semi-major and the length of the semi-minor axis of the ellipse $\frac{x^2}{144}+\frac{y^2}{169}=1$ are:

1. $26,12$
2. $13,24$
3. $12,26$
4. $13,12$

Q.

One focus of an Ellipse is (1, 0) with centre (0, 0). If the length of major axis is 6, its e =

1. $\frac{1}{4}$

2. $\frac{2}{3}$

3. $\frac{1}{3}$

4. $\frac{1}{2}$