SOLUTION: find the equation of a circle with center of origin, and tangent to the line 4x+3y=10

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Question 895788: find the equation of a circle with center of origin, and tangent to the line 4x+3y=10
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
One of the radii of the circle has an endpoint meeting the line 4x+3y=10 at a right angle. The LINE for this radius has slope and contains the point (0,0). I identified this slope through using an understanding of the standard form in which the line 4x+3y=10 was given.

Can you derive the equation of the line containing this radius which meets 4x+3y=10 at a right angle? When you do, then you have two equations of intersecting lines; and you can find the intersection point.

Once that is done, you have this endpoint and the other end point, (0,0), which form the perpendicular radius. Use Distance Formula to find and compute the value of the radius.

Can you do that, and then finish?
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

find the equation of a circle with center of origin, and tangent to the line 4x+3y=10


1) Find the equation of the radius line, using the point (0, 0), and m, or

   slope:  . This will result in the equation:



2) Solve 4x + 3y = 10 for y, and set this equation, and the equation, 

   equal to each other to determine the point at which the radius and the 

   tangent line to the circle, intersect.



3) Along with the intersecting point of the two lines, and the point (h, k), or (0, 0), use the 

   center-radius equation of a circle:  to determine the length of the radius.



4) Using the value of the length of the radius, squared, and the center point (h, k), or (0, 0), 

   write the equation of the circle, in center-radius form. 

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