Question

How do you graph `x^2+y^2+2x+2y=23`?

Answer 1

Just draw a circle with center at `(-1,-1)` and radius `5`.

Explanation:

General form of quadratic equation of a conic section is `ax^2+by^2+2hxy+2gx+2fy+c=0`.

As in given the equation `x^2+y^2+2x+2y=23`, the term `xy` is not there and coefficients of `x^2` and `y^2` are equal, this is the equation of a circle.

`x^2+y^2+2x+2y=23`

`hArr` `(x^2+2x+1)+(y^2+2y+1)=23+1+1`

`hArr` `(x+1^2)+(y+1)^2=25=5^2`

As this is the equation of a circle with center at `(-1,-1)` and radius `5`.

Hence to draw the graph of `x^2+y^2+2x+2y=23`, draw a circle with center at `(-1,-1)` and radius `5`