Question

Find the equation and centre of circle passing through the points (3,4),(3,2),(1,4)

Answer 1

this is the answer to your question

Answer 2

Step-by-step explanation :-

Take given A(3,4) , B(3,2) and C(1,4).

Let center of required circle is S(α,β)

We know that SA = SB = SC ⇒ SA² = SB² = SC²

Distance between two points (x₁,y₁) and (x₂,y₂) is $\bold{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$.

⇛ (α - 3)² + (β - 4)² = (α - 3)² + (β - 2)² = (α - 1)² + (β - 4)²

⇛ -4β + 12 = -4α + 4β - 4 = -4α + 8.

Solve the above equations.

Center of circle :

⇒ S(α,β) = S(2,3)

The radius of the spherical circle 'r' = SC = √1+1 = √2

Equation of required circle is :

⇒ (x - α)² + (y - β)² = r²

⇒ (x - 2)² + (y - 3)² = 2

∴ x² + y² - 4x - 6y + 11 = 0