Question

The equation x ^ 2 (y - 1) ^ 2 = 49 represents circle b is obtained by shifting circle a down 2 units in the xy-plane. which of the following equations represents circle b?

A) x ^2(y+2) ^2 =49
B) x ^2(y+2) ^3 =49
C) x ^2(y+2) =49
D) None of these

Answer 1

The equation that represents circle b, obtained by shifting circle a down by 2 units, is A) x^2(y + 2)^2 = 49.

Step-by-step explanation:

The equation x^2(y - 1)^2 = 49 represents a circle that can be obtained by shifting circle a down 2 units in the xy-plane. When you shift a circle down by 2 units, you adjust the y-coordinate in the equation by adding 2 to it because the center of the circle moves from (0, 1) to (0, -1). Hence, the modified equation becomes x^2(y + 2)^2 = 49.

Thus, the correct answer to the question 'which of the following equations represents circle b?' is A) x^2(y + 2)^2 = 49.