Question

Write the equation of the circle
with center (2,-5) and radius of 4.
*

Answer 1

`(x - 2) {}^(2) + (y + 5) {}^(2) = 16`

Explanation:

Equation of circle is:

`(x - h) {}^(2) + (y - k) {}^(2) = r {}^(2) \\`

Here (h,k) are the coordinates of center and r is radius

(h,k) =(2,-5)

r. = 4

plug in the values of h,k and r

`(x - 2) {}^(2) + (y - ( - 5)) {}^(2) = 4 {}^(2) \\ (x - 2) {}^(2) + (y + 5) {}^(2) = 16`

Answer 2

`(x-2)^2+(y+5)^2=16`

Explanation:

Equation of a circle

`(x-a)^2+(y-b)^2=r^2`

(where (a, b) is the center and r is the radius)

Given:

• center = (2, -5)
• radius = 4

Substitute the given values into the equation:

`\implies (x-2)^2+(y-(-5))^2=4^2`

`\implies (x-2)^2+(y+5)^2=16`