<s>[INST] Find the point where $3x-4y+25=0$ is a tangent to the circle $x^2+y^2=25$ Find the coordinates of the point where the line $3x-4y+25=0$ is a tangent to the circle $x^2+y^2=25$.
Can someone please show me the first few steps of solving the simultaneous equation?
 [/INST] $$
3x - 4y + 25 = 0\\
4y = 3x + 25\\
m = \frac34
$$
Differentiate circle equation $ x^2 + y^2 =25 $
$ \dfrac{dy}{dx}= -\dfrac xy = m = \dfrac 34 $
Solve for x and y to get,  $ x = \mp 3, y =\pm 4 $
Only the first set $ (-3,4)$ satisfies the given equation of straight line tangent.
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