Question:
find equation to the circle whose centre is (2,2) and which passes through point (4,5).
Answer:
The centre of the circle is (h,k)=(2,2)
Since the circle passes through point (4,5), the radius (r) of the circle is the distance between the point (2,2) and (4,5).
Thus, the equation of the circle is
(x−h)2+(y−k)2=r2
⇒ (x−2)2+(y−2)2=13
⇒x2−4x+4+y2−4y+4=13
⇒x2+y2−4x−4y+8=13
⇒x2+y2−4x−4y - 5=0
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