In terms of pi, what is the area of the circle defined by the equation 2x^2 + 2y^2 + 10x - 6y - 18 = 0?
+36916 If you rearrange the equation into the standard form of a circle....you will find r = sqrt(17.5)
pi r^2 = area = 17.5 pi
+532 this is a more helpful version of EP's solution:
rearranging terms, you get 2x^2+10x+2y^2-6y=18. completing the square, you get 2(x + 2.5)^2 + 2(y - 1.5)^2 = 18 + 4.5 + 12.5, or (x + 2.5)^2 + (y - 1.5)^2 = 17.5. Now it is just a matter of multiplying the right side by pi, so it is 35pi/2.
HOPE THIS HELPED!
+128474 2x^2 + 2y^2 + 10x - 6y - 18 = 0?
Divide through by 2 and rearrange
x^2 + 5x + y^2 - 3y = 9 complete the square on x and y
x^2 + 5x + 25/4 + y^2 - 3y + 9/4 = 9 + 25/4 + 9/4
Simplifying the right side, we have
17/2 + 9 = 35/2 this is r^2
So....the area = pi (35/2) = 17.5 pi units^2
