Question 767039
Q:
An equation of the line tangent to the graph of {{{25=x^2+y^2}}} at the point (3,4) is
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A:
Let {{{m[1]}}} be the slope of the line joining the center of the circle and the point of tangency.
{{{m[1]}}} = {{{(4 - 0)/(3 - 0)}}} = {{{4/3}}}
The slope of the tangent line is equal to {{{(-1)/m[1]}}} = {{{-3/4}}}.
The equation of the tangent line is {{{y - 4 = (-3/4)(x - 3)}}}.
ANSWER: {{{highlight(y = (-3/4)x + 25/4)}}}.
Here's the graph of the tangent line and the circle:
{{{drawing(300,300,-8,8,-8,8,grid(1),circle(0,0,5),line(-8,49/4,8,1/4))}}}