In terms of pi, what is the area of the circle defined by the equation 2x^2 + 2y^2 + 10x - 6y - 18 = 0?

Guest Jan 16, 2019

#1**+2 **

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

ElectricPavlov Jan 16, 2019

edited by
Guest
Jan 16, 2019

#2**0 **

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!

asdf335 Jan 16, 2019

#3**+1 **

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

CPhill Jan 16, 2019