Question

Number of ordered pairs (x, y) of real numbers satisfying the equation x2 + y2 - 24x - 26y +313=0 is equal
(A) infinite
(C)exactly one
(B)finite but more than one
(D) zero​

Answer 1

We have,

x² + y² - 24x - 26y + 313 = 0

x² + y² - 24x - 26y + 144 + 169 = 0

x² - 24x + 144 + y² - 26y + 169 = 0

(x - 12)² + (y - 13)² = 0

So the locus of the point satisfying this equation is a circle with the point P(12, 13) as its center and with the radius 0 units.

Well, such circle is not possible since the radius is 0, but there exists only the point P(12, 13) which is the unique solution.

Hence the equation has exactly one ordered pair solution of real numbers (x, y) and that is (12, 13).