Question

identify this conic section. $xy = 25$
parabola
ellipse
hyperbola
line
circle

Explanation:

Step1: Recall conic general form

The general quadratic conic equation is $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$. For $xy=25$, rewrite as $0x^2 + 1xy + 0y^2 + 0x + 0y -25 = 0$, so $A=0$, $B=1$, $C=0$.

Step2: Use discriminant test

The discriminant is $B^2 - 4AC$. Substitute values: $1^2 - 4(0)(0) = 1$.

Step3: Classify conic

When $B^2 - 4AC > 0$, the conic is a hyperbola.

Answer:

hyperbola