Home
Class 12
MATHS
Find the foci of the ellipse 25(x+1)^2+9...

Find the foci of the ellipse `25(x+1)^2+9(y+2)^2=225.`

Text Solution

Verified by Experts

The correct Answer is:
`(-1,2)(-1,-6)`
The given equation can be wirtten as `((x+1)^(2))/(9)+((y+2)^(2))/(25)=1`
which represents an ellipse whose center is `(-1,-2`) and semi-major and the minor are 5 and 3, respectively.
The eccentricity of the ellipse is given by
`9=251-e^(2)or e=(4)/(5)`
Shifting the origin at (-1,-2), the given reduces to
`(x^(2))?(9)+(y^(2))/(25)=1" "(1)`
where `x=X-1,y=Y-2" "(2)`
The coordinates of the foci (1) are `(X=0,Y=+-be)`, where `b=5, e=4//5, i.e., the foci of (1) (X=0,Y+-4)`.
Therefore, the cooridnates of the foci of the given ellipse are (-1,-2) and (-6,-6)
Promotional Banner

Similar Questions

Explore conceptually related problems

The distance between the foci of the ellipse 5x^(2)+9y^(2)=45 is

The foci of a hyperbola coincide with the foci of the ellipse (x^2)/(25)+(y^2)/9=1. Find the equation of the hyperbola, if its eccentricity is 2.

Find the centre of the ellipse 25x^(2)+9y^(2)-150x-90y+225=0 .

Find the axes, eccentricity, latus rectum and the coordinates of the foci of the hyperbola 25 x^2-36 y^2=225.

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide, then find the value of b^2

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide, then find the value

The foci of a hyperbola coincide with the foci of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 . If the eccentricity of the hyperbola is 2 , then the equation of the tangent of this hyperbola passing through the point (4,6) is

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide write the value of b^2dot

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of a. hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)