There is something wrong with the fifth question, and the quadratic term of y is missing. Such an equation would be a parabola. If the topic is right, the idea of this topic is as follows: If a point on the circle is still on the circle after symmetry, then a straight line passes through the center of the circle, and the coordinates of the center of the circle can be seen from the equation of the circle (such as (-2, -a/2) in the topic), and it is enough to substitute it into the linear equation to find a..

Question 6: The geometric meaning of this y/x is the slope of the line connecting a point on the circle with the origin. Just draw a picture and get a tangent. Connect the tangent point with the center of the circle, use the pythagorean method, and then find the tangent.

Question 19: Let the center of the circle be C(m, n) and the radius be r.

Then the equation of the circle is (x-m)2+(y-n)2=r2.

If the circle is tangent to the X axis, the absolute value of the ordinate of the center of the circle is the radius length.

∴ The circle equation can be simplified as x2-2mx+m2+y2-2ny=0.

From point A (0, 1), B (4, a) is on circle C.

Finishing (1-a) m2-8m+a2-a+16 = 0.

If only 1 circles satisfy the meaning of the problem, then there must be m and only one unique solution.

① When 1-a≠0 means a≠ 1.

△= 64-4( 1-a)(a2-a+ 16)= 0

Solve a=0

∴m2-8m+ 16=0,m=4

At this point, the equation of circle c is. . .

② When 1-a=0, that is, a= 1.

∴-8m+ 16=0,m=2，

The equation of the circle at this time is. . .

Question 22: The geometric meaning of y/x has been said before (y-b/x-a is the slope of the connecting line between point (x, y) and point (a, b) on the circle, and it is also obtained by tangent).

The geometric meaning of x2+y2 is the square of the distance from the point on the circle to the origin. The farthest and nearest methods to find the distance from the point outside the circle are the distance from the point outside the circle to the center plus the radius and minus the radius respectively.