A curve on the xoy plane passes through the point (2,3), and any line segment between the two coordinate axes is bisected by the tangent point According to the meaning of the topic, the intercept of the tangent of the curve at the point (x, y) on the two coordinate axes should be 2x and 2Y How do we get the intercept 2x and 2Y?

A curve on the xoy plane passes through the point (2,3), and any line segment between the two coordinate axes is bisected by the tangent point According to the meaning of the topic, the intercept of the tangent of the curve at the point (x, y) on the two coordinate axes should be 2x and 2Y How do we get the intercept 2x and 2Y?

From the midpoint formula: 2XM = XA + XB 2ym = Ya + Yb
When m is the moving point (x, y), the intercept of X axis is a (corresponding point is a (a, 0)); and the intercept of Y axis is B (corresponding point is B (0, b)):
2x=a+0 2y+0+b => a=2x b=2y
That is, the intercept on the coordinate axis is 2x and 2Y respectively