Question 1168322: A center is centered at (2, 1) and tangent to the line x+y=0. Find the equation of the circle
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source):
Answer by ikleyn(52852)  (Show Source):
You can put this solution on YOUR website! .
A  CIRCLE is centered at (2, 1) and tangent to the line x+y=0. Find the equation of the circle
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You have everything except the radius of the circle to write the standard equation of the circle.
So, all you need is to find the radius, which is the distance from the point (2,1) to the line x + y = 0.
There is a remarkable formula to calculate the distance from a given point to a given straight line in a coordinate plane.
Let the straight line in a coordinate plane is defined in terms of its linear equation
a*x + b*y + c = 0,
where "a", "b" and "c" are real numbers, and let P = ( , ) be the point in the coordinate plane.
Then the distance from the point P to the straight line is equal to
d =  .
Regarding this formula, see the lesson
The distance from a point to a straight line in a coordinate plane
in this site.
Your line is x + y = 0.
Substitute the given data a= 1, b= 1, c= 0, = 2, = 1 into the formula to get the distance under the question
 =  =  =  = 2.12132 (approximately).
Thus the distance and the radius of the circle is . Then the equation of the circle is
 +  =  . ANSWER.
Solved.
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