What is the area enclosed by the region defined by the equation x^2+y^2+10x+24y=0?

Guest Nov 15, 2019

#2

#4**+1 **

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?

Nirvana
Nov 15, 2019

#5**+1 **

Yeah I was trying to get the guest to reply because I was confused by "do the see"

CalculatorUser
Nov 15, 2019

#6**+1 **

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.

x^{2} + y^{2} + 10x + 24y = 0

Rearrange the terms.

x^{2} + 10x + y^{2} + 24y = 0

Add (10/2)^{2} which is 25 to both sides to complete the first square.

x^{2} + 10x + 25 + y^{2} + 24y = 25

Add (24/2)^{2} which is 144 to both sides to complete the second square.

x^{2} + 10x + 25 + y^{2} + 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

r^{2} = 169 , where r is the radius of the circle. And so

area of the circle = π r^{2} = 169π

hectictar Nov 15, 2019