SOLUTION: Find the equation of circle which touches x-axis at (3,0) and passes through the point (1,2).

Question 803155: Find the equation of circle which touches x-axis at (3,0) and passes through the point (1,2).
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
A strategy could be, find the line that the two given points define. The line contains the center of the desired circle. The equation for this line is (using formula for slope, and then starting from point-slope formula), y=-x+3.
This means that the center point for your desired circle is at some general (x, -x+3).

USE THE DISTANCE FORMULA between (x, -x+3) and each of the two given points; and equate the distances and solve for x. You may find two values. One will make sense and one will not make sense. WHY? Because you want the center which would agree with CONTAINING (1,2) and only TOUCHES (3,0). The circle center should be in quadrant 1.

Distance from center to (3,0) will then be the radius. Fill in the standard form, , center being (h,k).
I have not worked all the way through this, but only described a strategy to solve the problem.

Note: I suspect the center will also be contained on the vertical line, x=3. I say this because of "... touches the x axis..."
RELATED QUESTIONS
Find the equation of circle which touches x axis at (3,0) and passes through (2,3) (answered by Alan3354)

Find the equation of the circle which touches the X axis at a point (3,0) and passing... (answered by josgarithmetic)

find the equation for the circle which touches the x-axis at the point (2,0) and passes... (answered by Edwin McCravy)

Find the equation of a circle that passes through (2,0) and (8,0) and also touches the... (answered by ikleyn)

Determine the equation of the cubic polynomial which cuts the x-axis at x =1/2 , touches (answered by Fombitz)

Find the equation of the cirlcle which touches the x-axis at the point (3,0) and passes... (answered by josgarithmetic)

A circle passes through the Point (8,7) and touches the y-axis at the Point (0,3). Find... (answered by josgarithmetic)

find the equation of circle which touches xaxis at (4,0) and also passes through... (answered by jim_thompson5910)

Find the equation of the circle with centre (2,-3) which touches the x axis?? (answered by ewatrrr)