Question -
Answer -
Given:
Centre is (1, 2) andwhich passes through the point (4, 6).
Where, p = 1, q = 2
We need to find theequation of the circle.
By using the formula,
(x – p)2 +(y – q)2 = r2
(x – 1)2 +(y – 2)2 = r2
It passes through thepoint (4, 6)
(4 – 1)2 +(6 – 2)2 = r2
32 + 42 =r2
9 + 16 = r2
25 = r2
r = √25
= 5
So r = 5 units
We know that the equationof the circle with centre (p, q) and having radius ‘r’ is given by: (x – p)2 +(y – q)2 = r2
By substitute thevalues in the above equation, we get
(x – 1)2 +(y – 2)2 = 52
x2 –2x + 1 + y2 – 4y + 4 = 25
x2 + y2 –2x – 4y – 20 = 0.
∴ The equation of thecircle is x2 + y2 – 2x – 4y – 20 = 0.