SOLUTION: find standard equation of circle that has centre on the line 5x-2y= -21 and tangent to both co-ordinate axes

Algebra.Com
Question 1008377: find standard equation of circle that has centre on the line 5x-2y= -21 and tangent to both co-ordinate axes
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
STRATEGY: The equivalent linear equation, must be an equal distance from x-axis, (x,0) as from y-axis, (0,y), because the point on each axis this equal distance is a point of tangency ON EACH of the axes.

Distance from the center (x, (5/2)x+21/2 ) to x-axis and to y-axis must be equal, because each axis contains a tangency point. Use distance formula.

That is a described strategy, but not the actual solution.
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
find standard equation of a circle that has the center on the line 5x-2y= -21 and tangent to both co-ordinate axes.
--------------------------------------------------------------- 
Notice that the center of this circle lies on the bisector of the first quadrant angle, which is the line y = x.

So, the center is the intersection point of the straight line 5x - 2y = -21 and the straight line y = x.

In other words, to find the center, we should find the point on the line 5x - 2y = -21 with x = y. It has 

the coordinates (a,a) such that 5a - 2a = -21. Hence, 3a = -21 and a = -7. Thus the center is (-7,-7).

Then the equation of the circle is 

 = ,

or

 = .

It is not the unique solution.

The other solution can be found if another bisector y = -x of the II-IV quadrants is used. 
I don't want to go to this matter, but you can, if you want.


RELATED QUESTIONS

Find the standard equations of the circles that have centers on the line 5x – 2y = -21... (answered by Alan3354)
Write the equation of the circle satisfying the given condition, centre on y = x, tangent (answered by ikleyn)
please helppppppp: Find the equation of circle with centre (6,7) and tangent to the line (answered by scott8148)
Find the length of the intercepts of the circle 3x^2+3y^2-5x+3y=0 on the co-ordinate... (answered by KMST)
A circle whose centre lies on the line y=3x-1, touches both axes. Find the equation of... (answered by ikleyn)
.Find the equation of the smaller circle that is tangent to the axes and the circle... (answered by Fombitz)
Please find an equation of the circle that satisfies the given condition. Circle lies in... (answered by Alan3354)
Find an equation of the circle that satisfies the given conditions. Circle lies in the... (answered by Alan3354)
A circle is tangent to both the X and Y axes and is tangent to the line 3x+4y=60 at the... (answered by ikleyn)