Question

Which conic section does this equation represent?

Answer 1

Answer:

Hyperbola

Step-by-step explanation:

$x^2-4x-y^2+6y-9=5$

Lets write variables in square form using completing the square method

LEts group x  and y terms

$(x^2-4x)+(-y^2+6y)-9=5$

y^2 terms should be positive always, so we pull out negative sign from y^2

$(x^2-4x)-(y^2-6y)-9=5$

We have negative sign in the middle. so we will get equation in the form of

$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} =1$

If we have negative sign in the middle then it is an hyperbola

Answer 2

Answer:parabola

Step-by-step explanation: