Question

The radius of a circle y2+x2-14x-8y+56=0 is

Question 5 Select one:

-4

-3

3

4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the radius of the circle, we need to rearrange the equation of the circle into standard form: (x - h)^2 + (y - k)^2 = r^2.

Given equation: y^2 + x^2 - 14x - 8y + 56 = 0

Rearranging the equation: x^2 - 14x + y^2 - 8y = -56

Completing the square for x: (x^2 - 14x + 49) + y^2 - 8y = -56 + 49

Completing the square for y: (x^2 - 14x + 49) + (y^2 - 8y + 16) = -56 + 49 + 16

Rewriting the equation: (x - 7)^2 + (y - 4)^2 = 9

Comparing this equation with the standard form, we can see that the radius (r) is equal to 3.

Therefore, the correct answer is: 3.