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mathdad
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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?
Can someone get me started? Must I use the point (0, 0) here?
RTCNTC said: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 said: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?
RTCNTC said:The radius is the distance between the origin and given point.
MarkFL said: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
The equation of a circle through the origin is x² + y² = r², where r is the radius of the circle. This equation is derived from the Pythagorean theorem, where the distance from any point on the circle to the origin is equal to the radius.
A circle passes through the origin if the coordinates of the center point are (0,0) and the radius is greater than 0. This means that the equation of the circle will be x² + y² = r², where r is the radius. If the equation does not have the form of x² + y² = r², then the circle does not pass through the origin.
The origin is significant in the equation of a circle because it serves as the center point of the circle. This means that all points on the circle are equidistant from the origin, and the distance from any point on the circle to the origin is equal to the radius of the circle.
No, a circle through the origin cannot have a negative radius. The radius of a circle represents the distance from the center point to any point on the circle, and distance cannot be negative. Therefore, the radius of a circle through the origin must always be a positive value.
To graph a circle through the origin, plot the center point at (0,0) and then use the radius to plot points around the origin. You can also use the equation x² + y² = r² to find other points on the circle by substituting different values for x and solving for y, or vice versa. Once you have several points, you can connect them to create a smooth circle.