Question

Write each equation in standard form and determine the type of figure (circle, ellipse, hyperbola, parabola)

x^2 + 2x +1 + y^2 = 4


x^2 + y^2 - 6x -2y + 4 = 0

Answer 1

I think i know to identify but how do I get started with standard form

Answer 2

is this two problems?

Answer 3

yes

Answer 4

both are circles because the coefficient of the \(x^2\) and \(y^2\) terms are the same (they are both 1)
your job is to complete the square

Answer 5

I put in standard form

Answer 6

1) (x+1)^2+y^2=2^2 Circle of radius 2 and center (-1, 0)

Answer 7

First factorize the ecuations

In the first one consider (a+b)^2 = a^2+2ab+b^2
So
x^2 + 2x +1 + y^2 = 4
(x+1)^2+y^2=4

Then remember that the standar form for the ecuations if a circle of radious r and center (h, k) is
(x-h)^2 + (y-k)^1 = r^2

Here, h=-1 , k =0 and r =2.

The other one is basically the same.

Answer 8

thanks

Answer 9

2) (x-3)^2+(y-1)^2=(sqrt(6))^2 Circle radius sqrt(6) and center (3,1)

Answer 10

thanks universidad