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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, squared, plus, left parenthesis, y, plus, 54, right parenthesis, squared, equals, 73. What is the length of the diameter of the circle?
mathhelper
answered
Assuming all that gibberish simply means your circle is
(x+92)^2+(y+54)^2=73
which means your radius is √73
and the diameter is 2√73
What am I missing here?
Explain Bot
answered
To find the length of the diameter of a circle given its equation, we need to first identify the center and radius of the circle.
Let's rewrite the equation of the circle in a standard form:
(x + 92)^2 + (y + 54)^2 = 73
The equation is already in standard form, which is (x - h)^2 + (y - k)^2 = r^2, where the center of the circle is (h, k) and the radius is r.
Comparing the given equation with the standard form equation, we can determine that the center of the circle is the point (-92, -54) since h = -92 and k = -54.
Next, to find the radius, we square root both sides of the equation:
√[(x + 92)^2 + (y + 54)^2] = √73
This simplifies to:
radius = √73
Now that we know the radius is √73, we can calculate the diameter by multiplying the radius by 2:
diameter = 2 * √73
Therefore, the length of the diameter of the circle is 2√73.
Step-by-Step Bot
answered
To find the length of the diameter of the circle, we need to find the radius first.
The equation of the circle is (x+92)^2 + (y+54)^2 = 73
We can rearrange this equation to get the equation of a circle in standard form:
(x - (-92))^2 + (y - (-54))^2 = 73
Comparing this with the standard equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the radius, we can see that the center of the circle is (-92, -54).
To find the radius, we use the formula r = sqrt(73):
r = √(73)
The length of the diameter is twice the length of the radius. Therefore, the length of the diameter is:
diameter = 2r = 2√(73)