Question:
Find the equation of circle where radius is 5 and whose Centre lies on x axis and passing through the point (2,3)?
Answer:
Given, radius of circle is 5 and whose center lies on x-axis i.e. (a, 0)
Now, equation of the circle is:
(x - h)2 + (y - k)2 = 52
=> (x - a)2 + (y - 0)2 = 25
=> (x - a)2 + y2 = 25 .................1
Now, the equation of circle is passing through the point (2, 3)
=> (2 - a)2 + 32 = 25
=> (2 - a)2 + 9 = 25
=> (2 - a)2 = 25 - 9
=> (2 - a)2 = 16
=> 2 - a = ±4
=> a = 2 ± 4
=> a = -2, 6
Case1: when a = -2
From equation 1, we get
(x + 2)2 + y2 = 25
=> x2 + 4 + 4x + y2 = 25
=> x2 + y2 + 4x + 4 - 25 = 0
=> x2 + y2 + 4x - 21 = 0
Case2: when a = 6
From equation 1, we get
(x - 6)2 + y2 = 25
=> x2 + 36 - 12x + y2 = 25
=> x2 + y2 - 12x + 36 - 25 = 0
=> x2 + y2 - 12x + 11 = 0
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