Question

The equation of the circle whose center is at (4,4) and whose radius is 5 is?

Answer 1

Answer: The equation of the circle is $x^2+y^2-8x-8y+7=0.$

Step-by-step explanation: We are given to find the equation of a circle with center at (4, 4) and radius 5 units.

The standard equation of a circle with center at (g, h) and radius 'r' units is given by

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

Here, (g, h) = (4, 4) and r = 5.

Therefore, the equation of the circle is

$(x-4)^2+(y-4)^2=5^2\\\\\Rightarrow x^2-8x+16+y^2-8y+16=25\\\\\Rightarrow x^2-8x+y^2-8y+32=25\\\\\Rightarrow x^2+y^2-8x-8y+7=0.$

Thus, the equation of the circle is $x^2+y^2-8x-8y+7=0.$

Answer 2

(x – h)² + (y – k)² = r²

Fill in the variables

(x – 4)² + (y – 4)² = 25