Vertices of Ellipse

Q.

If the foci and vertices of an ellipse be (±1, 0) and ( ±2, 0) , then the minor axis of the ellipse os

1. 2

2. 4

3. 

4. 

Q. If $\mid z-1\mid +\mid z+3\mid \le 8$
, then the range of values of $\mid z-4\mid$
is

1. (0, 8)
2. [0, 8]
3. [1, 9]
4. [5, 9]

Q. If the vertices of the ellipse $9x^2+25y^2-18x+100y-116=0$ are the extremities of latus rectum of a parabola whose vertex is $(x_1,y_1)$ where $y_1>-2,$ then

1. length of latus rectum of the ellipse is $\frac{50}{3}.$
2. directrix of the parabola is $y-3=0.$
3. the smaller area enclosed by the parabola and the ellipse is $\frac{5}{6}(9\pi -20)$ sq. units.
4. the smaller area enclosed by the parabola and the ellipse is $\frac{5}{6}(9\pi -10)$ sq. units.

Q.

The vertices of the ellipse $\frac{(x+1{)}^2}{25}+\frac{(y-3{)}^2}{16}$ = 1 is

1. (3, 4)(-6, 3)

2. (4, 3)(-6, 3)

3. (5, 3)(-7, 3)

4. (6, 3)(-8, 3)

Q.

The equation of the ellipse whose vertices are ( ±5, 0) and foci are ( ± 4 , 0 ) is

1. 

2. 

3. None of these

4. 

Q. If the vertices of the ellipse $9x^2+25y^2-18x+100y-116=0$ are the extremities of latus rectum of a parabola whose vertex is $(x_1,y_1)$ where $y_1>-2,$ then

1. length of latus rectum of the ellipse is $\frac{50}{3}.$
2. directrix of the parabola is $y-3=0.$
3. the smaller area enclosed by the parabola and the ellipse is $\frac{5}{6}(9\pi -20)$ sq. units.
4. the smaller area enclosed by the parabola and the ellipse is $\frac{5}{6}(9\pi -10)$ sq. units.

Q.

The equation of the ellipse whose vertices are ( ±5, 0) and foci are ( ± 4 , 0 ) is

1. $25x^2+9y^2=225.$

2. $9x^2+25y^2=225.$

3. $3x^2+4y^2=192.$

4. None of these

Q.

The equation of the ellipse whose vertices are ( ±5, 0) and foci are ( ± 4 , 0 ) is

1. $9x^2+25y^2=225.$

2. $25x^2+9y^2=225.$

3. $3x^2+4y^2=192.$

4. None of these

Q. The equation of the ellipse whose vertices are (–4, 1), (6, 1) and one latus rectum is x – 4 = 0 is

1. $\frac{(x-1{)}^2}{25}+\frac{(y-1{)}^2}{16}=1$
2. $\frac{(x-1{)}^2}{16}+\frac{(y-1{)}^2}{25}=1$
3. $\frac{(x+1{)}^2}{25}+\frac{(y+1{)}^2}{16}=1$
4. $\frac{(x+1{)}^2}{16}+\frac{(y+1{)}^2}{25}=1$

Q. $S_1,S_2$ are foci of an ellipse of major axis of length $10$ units and $P$ is any point on the ellipse such that perimeter of triangle $P{S}_1{S}_2$ is $15$. Then eccentricity of the ellipse is:

1. $0.5$
2. $0.28$
3. $0.75$
4. $0.25$

Q. The equation of the ellipse whose vertices are (–4, 1), (6, 1) and one latus rectum is x – 4 = 0 is

1. 
2. 
3. 
4. 

Q. Let $A=(-4,0)$, $B=(-1,4)$. C and D are points which are symmetric to points A and B respectively with respect to y-axis, then the area of the quadrilateral ABCD is?

1. $8$ sq. units
2. $12$ sq. units
3. $20$ sq. units
4. $10$ sq. units

Q. The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x-$axis and vertices $C$ and $D$ lie on the parabola, $y=x^2-1$ below the $x-$axis, is

1. $\frac{4}{3\sqrt{3}}$
2. $\frac{4}{3}$
3. $\frac{2}{3\sqrt{3}}$
4. $\frac{1}{3\sqrt{3}}$

Q. The parabola $y^2-2x-6y+5=0$ has

1. Focus $\equiv (-\frac{3}{2},3)$
2. Vertex $\equiv (-2,3)$
3. Directrix $x=-\frac{5}{2}$
4. all of these