Question

What is the center, radius, general form, and standard form of `x^2 + y^2 - 2x +6y - 3 =0`?

Answer 1

General form is `(x-1)^2+(y+3)^2=(sqrt13)^2`.

This is the equation of a circle, whose center is `(1,-3)` and radius is `sqrt13`.

Explanation:

As there is no term in the quadratic equation `x^2+y^2-2x+6y-3=0` and coefficients of `x^2` and `y^2` are equal,

the equation represents a circle.

Let us complete the squares and see the results

`x^2+y^2-2x+6y-3=0`

`hArrx^2-2x+1^2+y^2+6y+3^2=1^2+3^2+3=13`

or `(x-1)^2+(y+3)^2=(sqrt13)^2`

It is the equation of a point which moves so that its distance from point `(1,-3)` is always `sqrt13` and hence equation represents a circle, whose radius is `sqrt13`.