What is the area enclosed by the region defined by the equation x^2+y^2+10x+24y=0?
+701 HAHA nice joke CU,
But guest....
what do you not understand about these? do you have a specific question that we can help you with that does not include any math problems?
+2864 Yeah I was trying to get the guest to reply because I was confused by "do the see"
+9479 This is the equation of a circle. See: https://www.desmos.com/calculator/z1xxnd2tgl
To get it into "standard form" as CU was saying, we need to complete both squares.
x2 + y2 + 10x + 24y = 0
Rearrange the terms.
x2 + 10x + y2 + 24y = 0
Add (10/2)2 which is 25 to both sides to complete the first square.
x2 + 10x + 25 + y2 + 24y = 25
Add (24/2)2 which is 144 to both sides to complete the second square.
x2 + 10x + 25 + y2 + 24y + 144 = 169
Factor both perfect square trinomials.
(x + 5)2 + (y + 12)2 = 169
Now the equation is in the form we want. So we can see
r2 = 169 , where r is the radius of the circle. And so
area of the circle = π r2 = 169π
