Question

Let \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \) be three points. If the centre of the circle passing through A, B, and C is \( (h, k) \), then \( 2k - 4 = \):

• A. 0
• B. 2
• C. -1
• D. 1

Hint:

Use the general equation of the circle and substitute the given points to find the relationship between \( k \) and other variables.

Answer 1

The Correct Option is D

We are given three points \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \). The equation of the circle passing through these points will have the general form: \[ x^2 + y^2 + Dx + Ey + F = 0 \] Substitute the coordinates of the three points into the equation and solve for \( D \) and \( E \), leading to \( 2k - 4 = 1 \). Thus, the correct answer is option (4), \( 2k - 4 = 1 \).