Question 1142123
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You didn't ask a question; I will assume you want to know how to find the equation of the circle.<br>
(1) The equation of a circle with center (h,k) and radius r is {{{(x-h)^2+(y-k)^2 = r^2}}}.  With center (0,0), the equation is {{{x^2+y^2 = r^2}}}.<br>I will guess that you knew that....<br>
So to find the equation of the circle, you need to find the radius of the circle.<br>
(2) A radius to a point of tangency is perpendicular to the tangent; it is therefore the shortest distance from the center of the circle to any point on the tangent.<br>
(3) There is a concise formula for the shortest distance from a given point to a given line.  You can use the given center (0,0) and the line 5x+12y=26 to find the radius. Then you will have all you need to write the equation of the circle.<br>
Here is the formula for the (shortest) distance from a point (m,n) to a line with equation Ax+By+C=0.  Note the equation of the line must be in that exact form.<br>
{{{abs((Am+Bn+C)/sqrt(A^2+B^2))}}}<br>
If you need more help to finish writing the equation, post a thank-you note describing what you have done on the problem or what part you are having difficulty with.