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Find the equation of a circle which is tangent to the y-axis and passes through the points (1, 5) and (8, -2).
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| A circle is tangent to the y-axis and passes thru (1, 5) and (8, -2). (Photo by Math Principles in Everyday Life) |
Since the given circle is tangent to the y-axis, then the radius is equal to h which is the x-coordinate of the center of a circle.
Since the two points of a circle are given, then we can use the distance of two points formula in order to get the radius of a circle as follows
We need to get another equation because the above equation consists of two variables as follows
Substitute the value of h from equation (1) to equation (2), we have
After equating each factor to zero, the values of k are 10 and 2.
If k = 10, then
Hence, the center of a circle is C (13, 10) and its radius is r = h = 13.
Therefore, the equation of a circle is
If k = 2, then
Hence, the center of a circle is C (5, 2) and its radius is r = h = 5.
Therefore, the equation of a circle is
