Question

find the equation of the circle which passes through the points (2,-2),(3,4) and whose centre lies on line x+y=2

Answer 1

Equation of the circle is (x – h)2 + (y – k)2 = r 2 ...(1)

Given, (h, k) lies on the line 3x + 4y = 7

∴ 3h + 4k = 7 ...(2)

Given, (1, – 2) lies on (1).

∴ (1 – h)2 + (– 2 – k)2 = r 2

⇒ (1 – h)2 + (2 + k)2 = r 2 ...(3)

Given, (4, – 3) lies on (1).

∴ (4 – h)2 + (– 3 – k)2 = r 2

⇒ (4 – h)2 + (3 + k)2 = r 2 ...(4)

From (3) and (4), we have



Solving (2) and (5), we get



When , we have


Using (4), we have



Equation of the circle is



 

 

hope it helps u

Answer 2

Let the centre of the circle be (h, k) and radius of the circle be r.

∴ Equation of the circle is (x – h)2 + (y – k)2 = r 2 ...(1)

Given, (h, k) lies on the line 3x + 4y = 7

∴ 3h + 4k = 7 ...(2)

Given, (1, – 2) lies on (1).

∴ (1 – h)2 + (– 2 – k)2 = r 2

⇒ (1 – h)2 + (2 + k)2 = r 2 ...(3)

Given, (4, – 3) lies on (1).

∴ (4 – h)2 + (– 3 – k)2 = r 2

⇒ (4 – h)2 + (3 + k)2 = r 2 ...(4)

From (3) and (4), we have



Solving (2) and (5), we get



When , we have



Using (4), we have



Equation of the circle is



 

 

hope it helps u