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Find the equation of a circle whose center on the y-axis, and passes through the origin and the point (4, 2).
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
In this problem, the center of a circle is unknown and we need to solve it. Since the two points of a circle are given, then we can solve for the coordinates of the center of a circle by using the distance of two points formula as follows
Since the given figure is a circle, then it follows that their distances from the center are equal as follows
Square on both sides of the equation, we have
Since the center of a circle is located along the y-axis, then it follows that h = 0.
Hence, the center of a circle is C (0, 5). The radius of a circle can be solved by using the distance of two points formula as follows
Therefore, the equation of a circle is
