Question 1099730
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YOU  DO  NOT  NEED  CALCULUS  to answer this question.


Elementary algebra  PLUS  Elementary geometry  is fully enough !.
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<pre>
The vector from the center (which is the coordinate origin) to the tangent point is (x,y) = (3,4).


Its slope is {{{4/3}}}.

The tangent line is perpendicular to the radius drawn to the tangent point.

Hence, the tangent line has the slope {{{-3/4}}}.


Then the equation of the tangent line is  y - 4 = {{{(-3/4)*(x-3)}}},  or, after multiplying both sides by 4,  4y - 16 = (-3)*(x-3),

or, equivalently,  3x + 4y = 25.


What's it.
</pre>

Solved.



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