Mathematics: Prove that the tangent at any point of a circle is perpendicular to the radius

Prove that the tangent at any point of a circle

kakesheco4210

06.11.2020

For this case we have the following system of equations:

$y = x ^ 2-6x + 12\\y = 2x-4$

Equating the equations:

$x ^ 2-6x + 12 = 2x-4\\x ^ 2-6x-2x + 12 + 4 = 0\\x ^ 2-8x + 16 = 0$

We look for two numbers that when multiplied, get 16, and when added together, get -8.

These numbers are -4 and -4.

$(x-4) (x-4) = 0\\(x-4) ^ 2 = 0$

So, the solution is x = 4

We look for the value of y:

$y = 2x-4\\y = 2 (4) -4\\y = 8-4\\y = 4$

Finally, the solution is: (4,4)

(4,4)

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