Question

Given a circle with its center at (-9, 2) and passing through the point (-3, -6), what does the graph of this circle look like on the coordinate plane?

a) Circle with a radius of 5 units
b) Circle with a radius of 8 units
c) Circle with a radius of 10 units
d) Circle with a radius of 13 units

Answer 1

The graph of the circle on the coordinate plane is a circle with a radius of 10 units. Hence, option C is correct.

Step-by-step explanation:

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is (-9, 2) and it passes through the point (-3, -6). To find the radius, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values, we get:

d = sqrt((-3 - (-9))^2 + (-6 - 2)^2) = sqrt(6^2 + 8^2) = 10

So, the radius of the circle is 10 units (c). The graph of this circle on the coordinate plane will be a circle centered at (-9, 2) with a radius of 10 units.