Question

What does the equation x^2 + y^2 + 2x +1 =0 represent ? Please explain .

a. a parabola
b. an ellipse
c. a point
d. a circle

Answer 1

It a circle because, the equation is a degree 2 equation. That is squared.

The coefficient of x^2 and y^2 are the same.

There is no term term xy.

And a parabola is of the form y^2 = 4ax or x^2 = 4ay.

And an ellipse is of the form: (x^2)/(a^2) + (y^2)/(b^2) = 1.

Answer 2

The equation represents a circle.

If you factorise the equation, you get:


`x^2 + y^2 + 2x +1 =0 \\(x+1)^2-1+(y)^2=0\\(x+1)^2+y^2=1`

This final equation shows the equation of a circle, as a circle's equation is given as:


`(x+a)^2+(y+b)^2=r^2`