Which equation represents a circle with a center at (–4, 9) and a diameter of 10 units? (x – 9)2 + (y + 4)2 = 25 (x + 4)2 + (y – 9)2 = 25 (x – 9)2 + (y + 4)2 = 100 (x + 4)2 + (y – 9)2 = 100

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

where

(h,k) is the center

r is the radius

In this problem we have

(h,k)=(-4,9)

r=10 units

substitute

Equation of circle is:

(x+4)²+(y-9)²=25

Step-by-step explanation:

the equation of a circle with center (h,k) and radius r is given by:

(x-h)²+(y-k)²=r²

Here, we are given (h,k)=(-4,9)

and diameter=10 units

⇒ radius=r=5 units

So, equation of circle will be:

(x+4)²+(y-9)²=5²

i.e. (x+4)²+(y-9)²=25

Hence, equation of circle is:

(x+4)²+(y-9)²=25

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step-by-step explanation: