Question

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

Answer 1

Hello!

The answer is:

The general form of the circle is:

$x^{2} -2x+y^{2} +4y=0$

Why?

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!