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Find the standard form of the equation of the circle with endpoints of a diameter at (4, 3) and (0, 1).
I think the midpoint must be found here.
If that's the case, let M = midpoint.
M = (2, 2)
I now need r.
Let r = the distance from any of the endpoints of the circle to the midpoint.
I will use the endpoint (0, 1).
r = sqrt{(0 - 2)^2 + (1 - 2)^2}
r = sqrt{5}
Plug r into x^2 + y^2 = r^2.
x^2 + y^2 = (sqrt{5})^2
My answer is x^2 + y^2 = 5.
Yes?
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What is the standard form of the equation of the circle whose radius is sqrt(5) and its center (0,0)?
It is:
x^2 + y^2 = 5
And this is your answer here though the center of your given circle is at M(2, 2) which you did well in finding it.
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What is the standard form of the equation of the circle whose radius is sqrt(5) and its center (0,0)?
It is:
x^2 + y^2 = 5And this is your answer here though the center of your given circle is at M(2, 2) which you did well in finding it.
Is it right or wrong? It's either yes or no....
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KerimF wrote:What is the standard form of the equation of the circle whose radius is sqrt(5) and its center (0,0)?
It is:
x^2 + y^2 = 5And this is your answer here though the center of your given circle is at M(2, 2) which you did well in finding it.
Is it right or wrong? It's either yes or no....
Ok, it is wrong.
The center of your circle is at (0, 0). It should be at M(2, 2) as you found out.
Last edited by KerimF (2024-03-03 01:38:21)
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FelizNYC wrote:KerimF wrote:What is the standard form of the equation of the circle whose radius is sqrt(5) and its center (0,0)?
It is:
x^2 + y^2 = 5And this is your answer here though the center of your given circle is at M(2, 2) which you did well in finding it.
Is it right or wrong? It's either yes or no....
Ok, it is wrong.
The center of your circle is at (0, 0). It should be at M(2, 2) as you found out.
Ok. Copy.
Let r = 5
(x - h)^2 + (y - k)^2 = r^2
(x - 2)^2 + (y - 2)^2 = 25
Yes?
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It is right.
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It is right.
Now I'm cooking with gas.
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