Chapter 10: Analytic Geometry

Identify each conic without completing the square or rotating axes.$x^2-6xy+9y^2+2x-3y-2=0$

For the ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$, the vertices are the points _____ and _____.

Identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes.

$4x^2-16x+16y+32=0$

Find a polar equation for the circle with center at the point $(0,4)$and radius 4. Graph this circle.

Answer Problems 9–11 using the figure.

The equation of the hyperbola is of the form

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

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

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x=t+2,y=\sqrt{t};t\ge 0$