General Equation of Ellipse

Q.

Foci of the Ellipse $25x^2+9y^2-150x-90y+225$ = 0 are

1. (3, 9) (3, 1)

2. (4, 9) (4, 1)

3. (6, 9) (5, 1)

4. (5, 7) (4, 7)

Q. 11. Vertices (0, +13), foci (0, +5)

Q. 12.Vertices仕6, 0), foci ± 4, 0)

Q. $P(a,b)$ is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$

Q.

The distance between a point P and the centre of a circle is 'd'. The given circles radius is r. Then what is the minimum distance between the circle and the point.

1. d-r

2. d+r

3. r-d

4. 2d-r

Q. Solve the given inequalities graphically:

Q. Let the sum of $n,2n,3n$ terms of an A.P. be $S_1,S_2$ and $S_3$, respectively, show that $S_3=3(S_2-S_1)$.

Q. The number of integral points which lies inside the ellipse whose vertices and foci are $(\pm 5,0)$ and $(\pm 4,0)$ respectively is

Q.

Consider an ellipse whose focus is at $(ae,0)$ and directrix along $(x=\frac{a}{e})$.
Find the equation of the ellipse if
$b^2=a^2(1-e^2)$

1. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

2. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

3. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=0$

4. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=-1$

Q. A rod $AB$ of the length $30$ units slips on the coordinate axes such that $A$ lies on $x-$axis and $B$ lies on $y-$axis. Then, the locus of $C$ if $BC=2AC$ is

1. $x^2+4y^2=400$
2. $4x^2+y^2=400$
3. $x^2+4y^2=100$
4. $4x^2+y^2=100$