Question

How do you graph `x^2 + y^2 - 8x - 10y + 5=0`?

Answer 1

To graph the equation `x^2+y^2−8x−10y+5=0`, draw a circle with center at `(4,5)` and radius `6`.

Explanation:

As the equation `x^2+y^2−8x−10y+5=0` is of degree `2` and coefficients of `x^2` and `y^2` are equal and that of `xy` is `0`, it is clearly an equation of a circle.

Let us convert it into sum of squares as follows

`(x^2−8x+16)+(y^2−10y+25)=16+25-5` or

`(x-4)^2+(y-5)^2=36` or

`(x-4)^2+(y-5)^2=6^2`

which is the equation of a circle with center at `(4,5)` and radius `6`.

Hence, to graph the equation `x^2+y^2−8x−10y+5=0`, draw a circle with center at `(4,5)` and radius `6`.

graph{(x^2+y^2-8x-10y+5)(x^2+y^2-8x-10y+40.95)=0 [-10, 18, -2, 12]}