# Eccentricity of Ellipse

## Trending Questions

**Q.**The eccentricity of the ellipse 4x2+9y2=36 is

- √53

- 12√3

- 1√3

- √56

**Q.**The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

- 1√2

- √32

- 2√3

- √23

**Q.**The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

- √5+12

- none of these
- √5−12
- √5−14

**Q.**If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to

- 13

- 1√3

- 1√2

- 2√23

**Q.**If a variable point P on an ellipse with eccentricity e is joined to it's focii S, S′.Then locus of incentre of △PSS′ is another ellipse whose eccentricity is

- √2e1+e
- √2e1−e
- √e1−e
- √e1+e

**Q.**The eccentricity of the conic 9x2+25y2=225 is

- 2/5

- 4/5

- 1/5
- 1/3

**Q.**Let the length of the latus rectum of an ellipse with its major-axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

- (4√2, 2√2)
- (4√2, 2√3)
- (4√3, 2√3)
- (4√3, 2√2)

**Q.**Let S(3, 4) and S′(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent of the ellipse is (1, −4), then the eccentricity of the ellipse is

- 45
- 57
- 713
- 513

**Q.**The equation of the ellipse, whose axes are of lengths 6 and 2√6 and their equations are x−3y+3=0 and 3x+y−1=0 respectively, is

- 29x2−6xy+21y2+6x−58y−151=0
- 21x2−6xy+29y2+58x−6y−151=0
- 29x2−6xy+21y2+6x−58y+151=0
- 21x2−6xy+29y2+6x−58y−151=0

**Q.**The eccentricity of the ellipse 25x2+16y2=400 is

- 3/5

- 1/3

- 2/5

- 1/5

**Q.**Find the eccentricity of the hyperbola 9y2−4x2=36

**Q.**Find the eccentricity equation of an ellipse whose latus-rectum is

(i) half of its minor axis

(ii) half of its major axis.

**Q.**Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

**Q.**

The eccentricity of the ellipse which meets the straight line x7+y2=1 on the axis of x and the straight line x3−y5=1 on the axis of y and whose axes lie along the axes of coordinates, is

none of these

3√27

2√37

√37

**Q.**

If the length of the major axis of an ellipse is $\frac{17}{8}$ times the length of the minor axis, then the eccentricity of the ellipse is

$\frac{8}{17}$

$\frac{15}{17}$

$\frac{9}{17}$

$\frac{2\sqrt{2}}{17}$

$\frac{13}{17}$

**Q.**If the ellipse x2a2+y2b2=1 is inscribed in a rectangle whose length to breadth ratio is 2:1 in such a manner that it touches the sides of rectangle, then the area of the rectangle is

- 4(a2+b27)
- 4(a2+b23)
- 12(a2+b25)
- 8(a2+b25)

**Q.**A point moves so that its distance from the point (2, 0) is always 13 of its distance from the line x−18=0. If the locus of the point is a conic, then

- Locus of the point will be x236+y232=1.
- Locus of the point will be x218+y216=1.
- Length of the latus rectum of the conic =323 units
- Length of the latus rectum of the conic =16√23 units

**Q.**The eccentricity of the ellipse 4x2+9y2+8x+36y+4=0 is

- 35

- √23

- 56

- √53

**Q.**If the length of latus rectum of a horizontal ellipse x2tan2α+y2sec2α=1(α≠π2) is 12, then the possible value(s) of α in (0, π) is/are

- π12
- π6
- 5π12
- 7π12

**Q.**

Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipse:

(i)4x2+9y2=1

(ii)5x2+4y2=1

(iii)4x2+3y2=1

(iv)25x2+16y2=1600

(v)9x2+25y2=225

**Q.**

An ellipse is described by using an endless string which is passed over two pins.

If the axes are $6cm$ and $4cm$, the length of the string and the distance between the pins are ____________

**Q.**The eccentricity of the ellipse represented by the equation 25x2+16y2−150x−175=0 is

- 25
- 35
- 45
- 15

**Q.**The eccentricity of the ellipse x2a2+y2b2=1 if its latus-rectum is equal to one half of its minor axis, is

- √32

- 12

- 1√2

- none of these

**Q.**Let AB be a line segment of length 4 units with A on line y=2x and B on the line y=x, the locus of middle points of all such line segments is a

- Parabola
- Ellipse
- pair of straight lines
- circle

**Q.**

Find the lengths of transverse axis and conjugate axis, eccentricity, the co-ordinates of foci, vertices, length of the latus-rectum, and equations of the directrices of the following hyperbola $16{x}^{2}-9{y}^{2}=-144$.

**Q.**

If for the ellipse $\left(\frac{{\mathrm{x}}^{2}}{{\mathrm{a}}^{2}}\right)+\left(\frac{{\mathrm{y}}^{2}}{{\mathrm{b}}^{2}}\right)=1$, the y-axis is the minor axis and the length of the latus rectum is one half of the length of its minor axis, then its eccentricity is

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{3}{4}$

$\frac{3}{5}$

**Q.**The points of intersection of the two ellipse x2+2y2−6x−12y+23=0 and 4x2+2y2−20x−12y+35=0

- lie on a circle centered at (−83, −3) and of radius 13√472 unit
- lie on a circle centered at (83, 3) and of radius 13√472 unit
- lie on a circle centered at (8, 9) and of radius 13√472 unit
- are not concyclic

**Q.**The equation of the ellipse which passes through origin and has its foci at the points (1, 0) and (3, 0), is

- 3x2+y2=12x
- 3x2+4y2=x
- x2+4y2=12x
- 3x2+4y2=12x

**Q.**Write the eccentricity of the ellipse 9x2+5y2−18x−2y−16=0

**Q.**If S and S are two foci of the ellipse x2a2+y2b2=1 and B is an end of the minor axis such that △BSS′ is equilateral, then write the eccentricity of the ellipse.