Question

Can someone please answer and provide an explanation for these problems?

Answer 1

32) (x+12)(2)+(y)(2)=25

Explanation:

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

(x-(-12)(2)+(y-0)(2)=5(2)

(x+12)+(y)=25

Answer 2

Answer(s):

(32) -
`(x +12)^2 + y ^2 = 25`

(33) -
`(x +2)^2 + (y+6 )^2 = 36`

(34) -
`(x -8)^2 + (y+1 )^2 = 100`

(35) -
`(x -13)^2 + (y+12 )^2 = 1`

Explanation:

To solve these types of problems, it is only a matter of memorizing the equation of a circle and plugging in values appropriately.

`\boxed{\left\begin{array}{ccc}\text{\underline{The Equation of a Circle:}}\\\\(x - h)^2 + (y - k)^2 = r^2\\\text{Where} \ r \ \text{is the radius of the circle and} \ (h,k) \ \text{is the center of the circle.}\end{array}\right}`

For the following problems, find the equation of a circle with the given information.

(32) -
`\text{Center at} \ (-12,0) \ \text{and a radius,} \ r=5`

(33) -
`\text{Center at} \ (-2,-6) \ \text{and a radius,} \ r=6`

(34) -
`\text{Center at} \ (8,-1) \ \text{and a radius,} \ r=10`

(35) -
`\text{Center at} \ (13,-12) \ \text{and a radius,} \ r=1`

Question #32:

`(x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-12))^2 + (y - 0)^2 = (5)^2\\\\\Longrightarrow \boxed{ (x +12)^2 + y ^2 = 25}`

Question #33:

`(x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-2))^2 + (y - (-6))^2 = (6)^2\\\\\Longrightarrow \boxed{ (x +2)^2 + (y+6 )^2 = 36}`

Question #34:

`(x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 8)^2 + (y - (-1))^2 = (10)^2\\\\\Longrightarrow \boxed{ (x -8)^2 + (y+1 )^2 = 100}`

Question #35:

`(x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 13)^2 + (y - (-12))^2 = (1)^2\\\\\Longrightarrow \boxed{ (x -13)^2 + (y+12 )^2 = 1}`

Thus, all problems have been solved.