a.maths 問題!!!

Q1.
Let equation of tangent be y = mx + c.
When x = 6, y = 2, 2 = 6m + c, c = 2 - 6m
so equation of tangent becomes y = mx + (2 - 6m).
Distance between center of circle to tangent = radius
so [0 - m(0) + 6m - 2]/sqrt [1^2 + m^2] = +/- 2
(6m - 2)^2 = 4(1 + m^2)
36m^2 + 4 - 24m = 4 + 4m^2
32m^2 - 24m = 0
8m(4m - 3) = 0
m = 0 or 3/4.
So the tangents are:
y = 2 or
y = 3x/4 + (2 - 18/4)
4y = 3x - 10.
Q2.
Center of circle is (2, 0), radius = sqrt 20.
Distance from (2,0) to 2x + y + 2 = 0 is
[2(2) + (0) + 2]/sqrt [ 2^2 + 1^2] = 6/sqrt 5 which is not equal to sqrt 20, so 2x + y + 2 = 0 is not a tangent to circle.
Q3.
Let tangent be x + y + c = 0.
Distance from center of circle (0,0) to line = radius = 5
c/sqrt(1^2 + 1^2) = +/- 5
c = +/- 5 sqrt 2.
so the tangents are
x + y + 5 sqrt 2 = 0 and
x + y - 5 sqrt 2 = 0.