Math  /  Geometry

QuestionWrite the standard form of the equation of the circle with the given center and radius. Center (7,2),r=3(7,2), r=3
Type the standard form of the equation of the circle.

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a circle, given its center and radius! Watch out! Don't mix up the signs of the center coordinates in the equation.

STEP 2

1. Recall the standard form
2. Plug in the values

STEP 3

Alright, let's **kick things off** by remembering what the standard form of a circle equation looks like.
It's (xh)2+(yk)2=r2(x-h)^2 + (y-k)^2 = r^2, where (h,k)(h,k) is the **center** of the circle, and rr is its **radius**.
This equation basically says, "Hey, the distance squared from any point (x,y)(x,y) on the circle to the center (h,k)(h,k) is always the **radius squared**!"

STEP 4

Now, let's **plug in** what we know!
Our center is (7,2)(7,2), so h=7h=7 and k=2k=2.
Our radius is r=3r=3.
Substituting these **values** into our standard form equation, we get (x7)2+(y2)2=32(x-7)^2 + (y-2)^2 = 3^2.

STEP 5

Let's **simplify** that last bit! 323^2 is just 33=93 \cdot 3 = 9.
So, our equation becomes (x7)2+(y2)2=9(x-7)^2 + (y-2)^2 = 9.

STEP 6

The standard form of the equation of the circle is (x7)2+(y2)2=9(x-7)^2 + (y-2)^2 = 9.

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