Question

Write the standard equation for the circle.

center (10, –6), r = 6



A- (x + 10)² + (y – 6)² = 6


B- (x + 6)² + (y – 10)² = 36


C (x – 10)² + (y + 6)² = 36


D- (x – 10)² + (y + 6)² = 6

Answer 1

The standard form of a circle is:

(x-h)^2+(y-k)^2=r^2, where r=radius and (h,k) is the center of the circle.

We are told that r=6 and the center is (10,-6) so

(x-10)^2+(y+6)^2=36

Answer 2

Answer:- C.
`(x-10)^2+(y+6)^2=36`

The standard equation for a circle is
`(x-a)^2+(y-b)^2=r^2`, where r is the radius and (a,b)= center of the circle such that a= abscissa and b= ordinate of center.

Given:- Center of circle=(10, –6) , radius r=6

Here abscissa of center a=10

ordinate of center b= -6

Substitute values of a, b and r in the standard equation of circle, we get

`(x-10)^2+(y-(-6))^2=6^2\\\Rightarrow(x-10)^2+(y+6)^2=36`

⇒ C is the correct answer.