The tangent of a point P on the parabola y = x2-3x has an inclination angle of 45 degrees. It intersects with two coordinate axes at two points a and B. the AOB surface of the triangle can be obtained

The tangent of a point P on the parabola y = x2-3x has an inclination angle of 45 degrees. It intersects with two coordinate axes at two points a and B. the AOB surface of the triangle can be obtained

Method 1: let the coordinates of the tangent point p be (m, m ^ 2-3m). By calculating the derivative of y = x ^ 2-3x, we obtain that y ′ = 2x-3, the slope of the tangent line passing through point P = 2m-3 = Tan 45 ° = 1, M = 2, m ^ 2-3m = 4-3 × 2 = - 2. The coordinates of the tangent point P are (2, - 2). The equation of the tangent line AB is y + 2 = X-2