First, 1. The tangent of a straight line to a circle means that the distance from the straight line to the center of the circle is equal to the radius. For this problem, it is the distance d = | a * 0+b * 0+c |/(a 2+b 2) (1/2) =1= r (Note:
2. the point P(x, y) is on the circle x 2+y 2 = 4. According to the topic form (y-4)/(x-4), we know that the geometric meaning of this formula is the slope of the line from point P(x, y) to point (4, 4)! We can set this line equation as y-4=k(x-4), and get kx-y+4-4k=0 after a little sorting. (The purpose of this step is to find the value of tangent slope with linear equation, then get the range of straight line slope from point P to (4,4), and then find the maximum value. ) Then the distance from the tangent to the center of the circle is d = | 0-0+4. K = [4+\-7 (1/2)]/2, that is, the range of slope is found by us, that is, the range of (y-4)/(x-4) is found by us.
We see that the slopes are all greater than zero, so the maximum value is the+sign of the slope!
In fact, this question is basically the same as the first one. If the positional relationship between a straight line and a circle is required, it will eventually be transformed into solving the distance from the center of the circle to the straight line D = | 0+0+C |/(A 2+B 2) (1/2) = (This step uses the known condition A 2+B 2 = 65438. 1=R, as soon as you see that the shortest distance from a straight line to the center of the circle is that the root number 2 is greater than the radius 1, it means that the straight line and the circle are separated!