Given the circle C: X & # 178; + Y & # 178; = 4, the tangent equation of the circle passing through the point (- 2,1) is? What is the answer and the difference between the tangent equation and the ordinary equation?

Given the circle C: X & # 178; + Y & # 178; = 4, the tangent equation of the circle passing through the point (- 2,1) is? What is the answer and the difference between the tangent equation and the ordinary equation?

Let the tangent equation be Y-1 = K (x + 2), that is, kx-y + 2K + 1 = 0
Then the distance from the center of the circle to the tangent is radius 2, then there is: | 2K + 1 | / radical (k ^ 2 + 1) = 2
4k^2+4k+1=4k^2+4
k=3/4
The tangent equation is 3x-4y + 10 = 0 and x = - 2

The equation of the circle whose center is m (- 1,1) and tangent to the line x-7y-3 = 0

If the circle is tangent to the straight line, the distance from the center of the circle to the straight line is the radius of the circle R
According to the distance formula from point to line:
R = (- 1-7-3) under absolute value / root sign (1 & # 178; + 7 & # 178;)
=11/√50
So the equation of a circle is:
(x+1)²+(y-1)²=121/50