Question

What is the equation of the circle with center (4. -4) that passes through the point (1, 0)?

(x - 4)2 + (y + 4)2 = 25
(x-4)2 + y - 4)2 = 25
(x+4)2 + (y + 4)2 = 5
(x-4)²-(y + 4)² = 25

Answer 1

The equation of the circle is (x - 4)^2 + (y + 4)^2 = 25

Step-by-step explanation:

To find the equation of a circle with a given center and a point on the circle, we can use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.

In this case, the center is (4, -4) and the point is (1, 0). The distance between the center and the point is equal to the radius of the circle. So, we have:

(1 - 4)^2 + (0 + 4)^2 = r^2

(-3)^2 + (4)^2 = r^2

9 + 16 = r^2

25 = r^2

Therefore, the equation of the circle is (x - 4)^2 + (y + 4)^2 = 25.

Answer 2

Correct answer: A

equation of a circle having a centre (4, -4):

(x-4)² + (y+4)² =r²

now, (1, 0) passes through the circle.

Then, (1-4)² + (0+4)² =r²

So, 9 + 16 =r² =25

(x-4)² + (y+4)² =25