The minimum distance between the point on the parabola y = - x2 and the line 4x + 3y-8 = 0 is () A. 14B. 43C. 85D. 3 | Math enthusiast | Mathematical art

The minimum distance between the point on the parabola y = - x2 and the line 4x + 3y-8 = 0 is () A. 14B. 43C. 85D. 3

Let a point on the parabola y = - x2 be (m, - m2), and the distance from the point to the straight line 4x + 3y-8 = 0 is | 4m − 3M2 − 8 | 5. The analysis shows that when m = 23, the minimum value is 43, so B

If y = x2 + 4x (x ≥ a) has an inverse function, then the minimum value of a is______ ．

If y = x2 + 4x (x ≥ a) has an inverse function, then y = x2 + 4x is a monotone function on [a, + ∞), a ≥ - 2

Given the square of X + the square of Y - 2xy-8x + 8y + 16 = 0, then X-Y is equal to

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