Equation of Circle Through Origin

[mathdad]

Find the equation of the circle passing through the origin with center (3, 5).

Can someone get me started? Must I use the point (0, 0) here?

 

[MarkFL]

Find the equation of the circle passing through the origin with center (3, 5).

Can someone get me started? Must I use the point (0, 0) here?

If the center of the circle is at (3, 5) and one of the points on the circle is (0, 0), then how can we find the radius of the circle? In a circle, just what is the radius? How it is defined?

 

[mathdad]

If the center of the circle is at (3, 5) and one of the points on the circle is (0, 0), then how can we find the radius of the circle? In a circle, just what is the radius? How it is defined?

The radius is the distance between the origin and given point.

 

[MarkFL]

The radius is the distance between the origin and given point.

The radius is the distance between the center of the circle and any point on the circle. Since we are given the center and a point on the circle, we can determine the radius. :D

 

[mathdad]

The radius is the distance between the center of the circle and any point on the circle. Since we are given the center and a point on the circle, we can determine the radius. :D

Let r = radius

r = sqrt{(3 - 0)^2 + (5 - 0)^2}

r = sqrt{3^2 + 5^2}

r = sqrt{9 + 25}

r = sqrt{34}

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

(x - 3)^2 + (y - 5)^3 = (sqrt{34})^2

(x - 3)^2 + (y - 5)^2 = 34

Correct?

 

[MarkFL]

Looks good to me. (Yes)

 

[mathdad]

Instead of posting every question in the David Cohen precalculus textbook, I will post essential questions, questions that every student should know how to solve before going to calculus 1. There is no time to waste.