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Tangent equation of a point a (2,4) on the outside of a circle x ^ 2 + y ^ 2 = 4 Using the formula of distance from point to line d = 2, K can't be solved
Center coordinates (0,0), radius = 2
When the line passing through point a is perpendicular to the X axis, the linear equation x = 2
The distance from the center of a circle to a straight line = | 0-2 | = 2 = radius. This straight line is the tangent of a circle, which satisfies the meaning of the problem
If the line passing through point a is not perpendicular to the x-axis, let the linear equation y-4 = K (X-2) (K ≠ 0)
kx-y+4-2k=0
The line is tangent to the circle, the distance from the center of the circle to the line = radius
|k·0-0+4-2k|/√[k²+(-1)²]=2
To absolute value sign, to root sign, finishing, get
4k=3
K = 3 / 4, the tangent equation is y-4 = (3 / 4) (X-2), after sorting, y = 3x / 4 + 5 / 2
In conclusion, there are two tangent equations: x = 2; y = 3x / 4 + 5 / 2
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