Question

identify the conic given by $\frac{(x - 10)^2}{36}-\frac{(y - 9)^2}{36}=1$
ellipse
parabola
circle
hyperbola

Explanation:

Step1: Recall the standard forms

The standard form of an ellipse is \(\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1\) (sum of two fractions). The standard form of a parabola has either \(x\) or \(y\) squared, not both. The standard form of a circle is \((x - h)^2+(y - k)^2=r^2\). The standard form of a hyperbola is \(\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1\) (difference of two fractions).

Step2: Compare with given equation

The given equation is \(\frac{(x - 10)^2}{36}-\frac{(y - 9)^2}{36}=1\), which is in the form \(\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1\) (difference of two fractions).

Answer:

hyperbola