How do you determine circle, parabola, ellipse, or hyperbola from equation $x^2 + y^2 - 16x + 18y - 11 = 0$ ?

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Answer 1 · 2015-11-30T12:45:24

The equation is of a circle of radius $sqrt(156)$ centered at $(8, -9)$

Step 1: Group $x$ 's and $y$ 's

$x^2 - 16x + y^2 + 18y = 11$

Step 2: Complete the square for both $x$ and $y$

$x^2 - 16x + 64 + y^2 + 18y + 81 = 11 + 64 + 81$

$=>(x - 8)^2 + (y + 9)^2 = 156$

Step 3: Compare to the standard forms of conic sections

![https://www.pinterest.com/pin/429953095650353121/](useruploads.socratic.org)

Note that the above equation matches the formula for a circle with $h = 8$ , $k = -9$ , and $r = sqrt(156)$

Thus the equation is of a circle of radius $sqrt(156)$ centered at $(8, -9)$

How do you determine circle, parabola, ellipse, or hyperbola from equation x^2 + y^2 - 16x + 18y - 11 = 0x^2 + y^2 - 16x + 18y - 11 = 0?