Exam 10: Conic Sections

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $64 x^{2}+y^{2}-384 x+512=0$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{(y-2)^{2}}{49}-\frac{(x+2)^{2}}{64}=1$

Graph the circle. State the center and radius of the circle - $(x-1)^{2}+(y-1)^{2}=7$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{y^{2}}{49}-\frac{x^{2}}{4}=1$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $(-7,-5)$ and $(7,1)$

Find the foci of the ellipse. Round to the nearest tenth if necessary. - $\frac{(\mathrm{x}+11)^{2}}{81}+\frac{(\mathrm{y}-13)^{2}}{196}=1$

Graph the circle. State the center and radius of the circle - $(x-5)^{2}+(y+6)^{2}=9$

Find the standard-form equation of the ellipse. -

Find the vertex of the parabola by completing the square. - $y=-x^{2}-2 x-4$

Solve the system by the substitution method. - $x^{2}+y^{2}=9$ $\mathrm{y}=\mathrm{x}^{2}-3$

Find an equation of the circle with the given center and radius. -Center $(0,10)$ , radius $\sqrt{5}$

Find the foci of the ellipse. Round to the nearest tenth if necessary. - $\frac{(x-6)^{2}}{49}+\frac{(y+7)^{2}}{16}=1$

Find the standard-form equation of the ellipse. -

Graph the parabola. State the vertex of the parabola. - $x=-y^{2}+2 y+2$

Graph the circle. State the center and radius of the circle - $x^{2}+y^{2}-4 x-2 y-4=0$

Solve the problem. -

Find the equation of the circle. - $(x-3)^{2}+(y+5)^{2}=4$

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{(x+6)^{2}}{16}+\frac{(y+5)^{2}}{4}=1$

Solve. -A bridge with a semi- elliptical arch extends over a river as shown. Find an equation of the ellipse that represents the arch of the bridge.

Find the standard-form equation of the ellipse. -