The tangent equation of a (2,1) - direction circle x ^ 2 + y ^ 2 = 4 is rt | Math enthusiast | Mathematical art

The tangent equation of a (2,1) - direction circle x ^ 2 + y ^ 2 = 4 is rt

1. If the slope of the line does not exist
From l over a (2,1), we get l: x = 2,
It is verified that it is tangent to the circle X & sup2; + Y & sup2; = 4
2. If the slope of the line exists, let l be K
Let L: y = kx-2k + 1
From the tangent of L to the circle X & sup2; + Y & sup2; = 4, we obtain | 1-2k | / √ (1 + K & sup2;) = 2
So, (1-2k) & sup2; = 4 (1 + K & sup2;)
That is, 1-4k + 4K & sup2; = 4 + 4K & sup2;
K = - 3 / 4
So, l: y = - 0.75x + 2.5
In conclusion, the tangent equation of a (2,1) - direction circle x ^ 2 + y ^ 2 = 4 is x = 2 or y = - 0.75x + 2.5

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