The equation `(x^2 - a^2)^2 + (y^2 - b^2)^2 = 0` represents points

Options

A. which are collinear
B. which lie on a circle with centre at (0, 0)
C. which lie on a circle with centre at (a, b)
D. none of these

Answer

B

Explanation

We have,
`(x^(2)-a^(2))^(2)+(y^(2)-b^(2))^(2)=0`
`rArr x^(2)-a^(2)=0` and `y^(2)-b^(2)=0rArrx=pma` and (-a, -b).
Clearly, these points lie on a circle `x^(2)+y^(2)=a^(2)+b^(2)` having centre at the origin.