91Ó°ÊÓ

Path of a Projectile \(\quad\) A projectile moves so that its position at any time \(t\) is given by the equations $$x=60 t \text { and } y=80 t-16 t^{2}$$ Graph the path of the projectile, and find the equivalent rectangular equation. Use the window \([0,300]\) by \([0,200]\)

Decide whether each equation has a circle as its graph. If it does, give the center and radius. $$x^{2}+4 x+y^{2}-8 y+32=0$$

CHECKING ANALYTIC SKILLS Graph each hyberbola by hand. Give the domain and range. Give the center in Exercises \(55-61 .\) Do not use a calculator. $$x^{2}-y^{2}=1$$

Alternative Parametric Forms Give two parametric representations of the line through the point \(\left(x_{1}, y_{1}\right)\) with slope \(m\)

CHECKING ANALYTIC SKILLS Graph each hyberbola by hand. Give the domain and range. Give the center in Exercises \(55-61 .\) Do not use a calculator. $$9 x^{2}-4 y^{2}=1$$

Decide whether each equation has a circle as its graph. If it does, give the center and radius. $$x^{2}-2 x+y^{2}+4 y=0$$

Alternative Parametric Forms Give two parametric representations of the parabola \(y=a(x-h)^{2}+k\)

Decide whether each equation has a circle as its graph. If it does, give the center and radius. $$4 x^{2}+4 x+4 y^{2}-4 y-3=0$$

CHECKING ANALYTIC SKILLS Graph each hyberbola by hand. Give the domain and range. Give the center in Exercises \(55-61 .\) Do not use a calculator. $$25 y^{2}-9 x^{2}=1$$

Decide whether each equation has a circle as its graph. If it does, give the center and radius. $$9 x^{2}+36 x+9 y^{2}=-32$$