Question

A circle is centered at (5, −9) and has a radius of 12. Which of the following is the equation for this circle?

Answer 1

Answer:

$\boxed {\boxed {\sf (x-5)^2+(y+9)^2=144}}$

Step-by-step explanation:

The standard form for the equation of a circle is:

$(x-h)^2+(y-k)^2=r^2$

where (h,k)  is the center of the circle and r is the radius.

For this circle, the center is (5, -9) and the radius is 12. Therefore:

$h= 5 \\k= -9 \\r=12$

Substitute the values into the formula.

$(x-5)^2+(y-(-9))^2=(12)^2$

Distrubute the -1 into the -9.

• -(-9)= -1*-9= 9

$(x-5)^2+(y+9)^2=(12)^2$

Solve the exponent.

• (12)²= 12*12=144

$(x-5)^2+(y+9)^2=144$

The equation for the circle with a center (5,-9) and radius of 12 is (x-5)²+(y+9)²=144

Answer 2

Based on the calculations, the equation of this circle in standard form is equal to (x - 5)² +(y + 9)² = 144.

The equation of a circle.

Mathematically, the standard form of an equation of a circle is given by;

(x - h)² +(y - k)² = r²

Where:

• h and k represents the coordinates at the center.

• r is the radius of a circle.

Given the following data:

• Coordinates (h, k) = (5, -9).

• Radius = 12.

Substituting the given parameters into the formula, we have;

(x - 5)² +(y - (-9))² = 12²

(x - 5)² +(y + 9)² = 144

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