Question 139720: Show algebraically that the line 3x+2y=-4 passes through the center of the circle given by the equation x^2+y^2-4x+10y+19=0. HELP:)
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! First, to find the center of the circle, you want to get your equation into the standard form for a circle with center at (h, k) and radius, r.
To do this, you must "complete the square" in the x- and y-terms of your equation.
 Group the x- and y-terms together.
 Now subtract 19 from both sides.
 Next, complete the squares in the x- and y-terms by adding the square of half the x-coefficient and the square of half the y-coefficient to both sides of the equation.
 Factor the x- and y-terms on the left side and simplify the right side.
 now compare this with the general form:
...and you can see that the center of the circle, (h, k) is (2, -5)
Now you need to see if the point, (2, -5) satisfies the given equation:
 Substitute x = 2, and y = -5.
 Simplify.
 So the answer is yes, the line does pass through the center of the circle.!
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