Write the equation (x - 1) ^2 + (y + 2)^ 2 = 5 in general form.

Question

asked Sep 18, 2020 49.4k views

1 Answer

Kaleb Pederson · Answer 1 · 2020-09-24T10:29:47+0000

The answer is:

The general form of the circle is:

x^(2) -2x+y^(2) +4y=0

We are given the standard form of a circle, so, to calculate the general form, we need to solve notable products.

We must remember the way to solve the notable product:

$(a+b)^(2)=a^(2)+2ab+b^(2) \\\\(a-b)^(2)=a^(2)-2ab+b^(2)$

So,

We are given the equation:

(x-1)^(2)+(y+2)^(2)=5

Then, solving the notable products, and adding/subtracting like terms, we have:

$x^(2) -2*1x+1+y^(2)+2*2y+4=5\\x^(2) -2x+1+y^(2) +4y+4=5\\\\x^(2) -2x+y^(2) +4y+1+4-5=0\\\\x^(2) -2x+y^(2) +4y=0$

Hence, have that the general form of the circle is:

x^(2) -2x+y^(2) +4y=0

Have a nice day!