Question

A circle in the xyxyx, y‑plane has the equation (x+92)^2+(y+54)^2=73(x+92) 2 +(y+54) 2 =73left parenthesis, x, plus, 92, right parenthesis, start superscript, 2, end superscript, plus, left parenthesis, y, plus, 54, right parenthesis, start superscript, 2, end superscript, equals, 73. What is the length of the diameter of the circle?

Answer 1

Remember that the circle formula is; (x – h) 2 + (y – k) 2 = r 2 If you end up with an equation like (x + 92

Answer 2

Answer:

Diameter of the circle is $2\sqrt{73}$.

Explanation:

The given equation is

$(x+92)^2+(y+54)^2=73$        ..... (1)

We need to find the length of the diameter of the circle.

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$      ....(2)

where, (h,k) is center and r is radius.

On comparing (1) and (2) we get

$h=-92,k=-54,r^2=73\Rightarrow r=\sqrt{73}$

Radius of the circle is $r=\sqrt{73}$.

Diameter of the circle is twice of its radius.

$d=2r=2(\sqrt{73})=2\sqrt{73}$

Therefore, the diameter of the circle is $2\sqrt{73}$.