Question

1. what is the equation of a circle that has a diameter of 10 units if its center is at (3,8)?

$(x - 3)^{2}+(y - 8)^{2}=100$
$(x + 3)^{2}+(y + 8)^{2}=25$
$(x + 3)^{2}+(y + 8)^{2}=100$
$(x - 3)^{2}+(y - 8)^{2}=25$

Explanation:

Step1: Find radius from diameter

Radius $r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5$

Step2: Get circle equation form

Standard form: $(x-h)^2 + (y-k)^2 = r^2$, center $(h,k)=(3,8)$

Step3: Substitute values

$(x-3)^2 + (y-8)^2 = 5^2 = 25$

Answer:

D. $(x - 3)^2 + (y - 8)^2 = 25$