## Question

The foci of the conic 25*x*^{2} +16*y*^{2} – 150*x* = 175 are

### Solution

The given conic can be re-written as

Shifting the origin at (3, 0) without rotating the coordinates axes,

We have,

The equation of the ellipse with reference to new axes is

Comparing this equation with the standard equation

.

Let *e* be the eccentricity of the given conic. Then,

.

The coordinates of foci with respect to new origin are

Substituting these in (i), we obtain (3, ±3) as the coordinates of foci.

#### SIMILAR QUESTIONS

The length of the axes of the conic 9*x*^{2} + 4*y*^{2} – 6*x* + 4*y* + 1 = 0 are

The eccentricity of the ellipse

If the eccentricities of the two ellipse

are equal, then the value , is

The curve represented by the equation

, is

The equation of the ellipse whose axes are along the coordinate axes, vertices are (±5, 0) are foci at (±4, 0), is

The equation of the ellipse whose axes are along the coordinate axes, vertices are (0, ±10) and eccentricity *e* = 4/5, is

If the latusrectum of an ellipse is equal to one half of its minor axis, then the eccentricity is equal to

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latusrectum, is

The equation of the circle drawn with the two foci of as the end-points of a diameter, is

The foci of the ellipse are