Question 1199583
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ANSWER: B<br>
You won't learn anything from this if we solve the problem for you, so I will outline how you can get the answer and let you do the work.<br>
Let (x,y) be a point on the circle.<br>
The slope of the line from (15,15) to (x,y) is {{{(15-y)/(15-x)}}}.
The slope of the radius of the circle from the center (0,0) to (x,y) is {{{y/x}}}.<br>
A tangent and a radius to the point of tangency are perpendicular, so the product of their slopes is -1:<br>
{{{(15-y)/(15-x)(y/x)=-1}}} [1]<br>
Work with that equation until you get to the point where the equation is {{{x^2+y^2=A}}} where A is an expression in x and y.<br>
We also know {{{x^2+y^2=100}}} [2]<br>
so<br>
{{{A=100}}} [3]<br>
Solve equation [3] for y in terms of x and substitute in [2] to get an equation in x alone.<br>
Use a graphing calculator or similar tool to find the coordinates of the point of tangency.<br>
Note that, by the symmetry of the problem, if one of the points of tangency is (a,-b), then the other point of tangency is (-b,a).<br>
Use the two points of tangency and the fixed point (15,15) to find that the equations of the tangents are as given in answer choice B.<br>