SOLUTION: Find the equation of the circle if it is tangent to the line x+y=2 at point (4,-2) and the center at x-axis.

Question 678416: Find the equation of the circle if it is tangent to the line x+y=2 at point (4,-2) and the center at x-axis.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

(h,k)-center and r radius
given:
given:
the circle if it is tangent to the line at point (,) and the center at

find the equation of the circle:
Let ... C(,) be the center.
Also, let the line L : touch
this circle at the point A(,)
Line has slope
and slope of seg AC is .
Since line L is perpendicular to segment AC,

Hence, C ≡ (,) ≡ (,)
and
.
Hence, by Center-Radius Form, eq of circle is:

......... your answer

RELATED QUESTIONS
Find the equation of the circle tangent to the line 5x + y = 3 at the point (2, -7) and... (answered by Alan3354,Edwin McCravy)

Find the equation of a circle is tangent to the line -x+y+4=0 at the point (3, -1), and... (answered by MathLover1)

how to solve this find the equation of the circle describe here.. {{the circle is... (answered by scott8148)

1.) the circle is tangent to the line y=3-5x at the point (2,-7) whose center is on the (answered by greenestamps)

Find the equation of the circle if the circle is tangent to the line -x y 40 at the point (answered by Alan3354)

A circle is tangent to the line 3x-4y -4 = 0 at the point (-4,-4) and the center is on... (answered by robertb,greenestamps,ikleyn)

If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is an (answered by Edwin McCravy)

Find the general equation of the circle, if the circle is tangent to the line -3x+2y+1=0... (answered by MathLover1)