The Foci Of The Conic 25x2 +16y2 – 150x = 175 Are

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Question

The foci of the conic 25x² +16y² – 150x = 175 are

medium

Solution

Correct option is

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.

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