Mathematical quadratic function + circle. Teach me In the same rectangular coordinate system, it is known that the parabola y = 1 / 4x ^ - x + K intersects the Y axis at B (0,1), the point C (m, n) is on the parabola, and the circle m with diameter BC just passes through vertex a The value of K is 1 2. Find the value of point C What is vector theorem? How did (m-2, n) * (- 2, 1) come from

Mathematical quadratic function + circle. Teach me In the same rectangular coordinate system, it is known that the parabola y = 1 / 4x ^ - x + K intersects the Y axis at B (0,1), the point C (m, n) is on the parabola, and the circle m with diameter BC just passes through vertex a The value of K is 1 2. Find the value of point C What is vector theorem? How did (m-2, n) * (- 2, 1) come from

Vertex A: (2,0)
Take BC as the diameter to pass a, so ∠ BAC = 90“
According to the vector theorem, (m-2, n) * (- 2,1) = - 2m + 4 + n = 0
So n = 2m + 4
The equation y = 1 / 4m ^ - M + 1 = n = 2m + 4 is brought in
Find m, and then find n