Question 1142123: please help me understand this and help me answer it
The circle is tangent to line 5x + 12y= 26 and the center is at the origin Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
You didn't ask a question; I will assume you want to know how to find the equation of the circle.
(1) The equation of a circle with center (h,k) and radius r is . With center (0,0), the equation is . I will guess that you knew that....
So to find the equation of the circle, you need to find the radius of the circle.
(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.
(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.
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.
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.
