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Point p is moving some math problems.
1, the equation that the intersection point p is perpendicular to the tangent is Y= (root number 3) x.

Then the slope of the tangent is 1(- root number 3), and the point p can be found by substituting it into the equation.

2 .. If I don't do the second question, it is estimated that my sister won't be able to do it in three years, and there is no pen and paper in her hand.

Take advantage of all conditions. The coordinate of point m is (x, y). The coordinates of point P are (X 1, Y 1). According to the fact that m is the midpoint of AP, we can get 2X=X 1+4 and 2Y=Y 1. Then x 1, y666.

(2X-4)^2+(2Y)^2=4.

The second little question is similar to the first one.

Draw a picture in the third small problem, using the vertical diameter theorem.

It is more intuitive to draw pictures by analyzing geometric problems. Draw a sketch first and see what conditions can be used. Most tangent conditions are intersection plus a negative reciprocal slope.