Question

State the coordinates of the center and the measure of the radius of the circle with equation (x-1)^2+(y-4)^2=9 then graph the equation

Answer 1

Explanation:

We are given the equation:

`(x-1)^(2) +(y-4)^(2) =9`

the baseline equation for a graph is:
(x-h)²+(y-k)²=r²

with (h,k) being the center, and r being the radius.

Given this, we can find out the center and radius:

center=(1,4) (tip: take the inverse h and k)

radius= 3 (tip: find the square root of r²)

See attachment for graphed circle:

To graph the equation, we need the center, (1,4) and the radius, 3.

First, plot the center on the graph. The x value will be 1 and the y value will be 4. Next, move 3 units out either up, down, left, or right to graph a point that falls on the circle. This gives you the radius. When done, you should have a circle that has a center, and a diameter of 6 units, and a radius of 3.

Hope this helps! :)

Answer 2

The center of the circle is (1, 4), and the radius is 3 units.

Explanation:

he equation (x-1)^2 + (y-4)^2 = 9 represents a circle with center (1, 4) and a radius of 3 units.

To graph the equation, plot the center point (1, 4) on a coordinate plane. Then, draw a circle around this point with a radius of 3 units. The circle should pass through points (4, 4), (1, 7), and (-2, 4) on the coordinate plane. The center of the circle is (1, 4), and the radius is 3 units.