Question

What is the standard form of the equation for this circle?

Answer 1

Hello,

Center:(4,-5); radius=5.5

Equation is (x-4)²+(y+5)²=5.5²

5.5²=30.25
Answer B

Answer 2

Answer: The correct option is

(B)
`(x-4)^2+(y+5)^2=30.25.`

Step-by-step explanation: We are given to select the correct standard form of the equation of the circle shown in the figure.

The standard equation of a circle with center at the point (h, k) and radius of length r units is given by

`(x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)`

For the given circle, as noted from the figure, we have

center, (h, k) = (4, -5) and radius, r = 5.5 units.

Therefore, from equation (i), we get

`(x-4)^2+(y-(-5))^2=(5.5)^2\\\\\Rightarrow (x-4)^2+(y+5)^2=30.25.`

Thus, the required equation of the given circle is
`(x-4)^2+(y+5)^2=30.25.`

Option (B) is CORRECT.