Question

Find the equation of the circle passing through the points (2,3) and (-1,1) and
whose centre is on the line x - 3y - 11 = 0​

Answer 1

Step-by-step explanation:

Let the equation of the required circle be (x – h)2 + (y – k)2 = r2. Since the circle passes through points (2, 3) and (–1, 1), (2 – h)2 + (3 – k)2 = r2 ………………………….. (1)

(–1 – h)2 + (1 – k)2 = r2 ……………… (2) Since the centre (h, k) of the circle lies on line x – 3y – 11 = 0, h – 3k = 11 …………………………………………….. (3)

From equations (1) and (2), we obtain

(2 – h)2 + (3 – k)2 = (–1 – h)2 + (1 – k)2

⇒ 4 – 4h + h2 + 9 – 6k + k2 = 1 + 2h + h2 + 1 – 2k + k2

⇒ 4 – 4h + 9 – 6k = 1 + 2h + 1 – 2k ⇒ 6h + 4k = 11 … (4)

On solving equations (3) and (4), we obtain ℎ=7/2 and =−5/2. On substituting the values of h and k in equation (1), we obtain

*the first image shared*

Thus, the equation of the required circle is

*the second image shared*