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.