Conic Sections
"Find the center of the hyperbola "
9x^2-16y^2-18x-64y-199=0.
9(x^2-2x+__)-16(y^2-4y+__)=199+__+__
" "implies" " 9(x^2-2x+1)-16(y^2-4y+64)=199+9-64
9(x-1)^2-16(y+2)^2=144
((x-1)^2)/16-((y+2)^2)/9=1" "implies" "center(1,-2)
"Write the parametric equations "
x=2+3t and y=1-4t" as an equation in rectangular form."
x=2+3t" "implies" "t=(x-2)/3
y=1-4((x-2)/3)" "implies" "y=1-4/3x+8/3" "implies" "y=-4/3x+11/3
"Write the equation "2x+y=3" in polar form."
x=rcostheta and y=rsintheta
2(rcostheta)+(rsintheta)=3
r(2costheta+sintheta)=3
r=3/(2costheta+sintheta)
"Solve "{(x,-,7y,+,8z=,85),(,,y,-9z,=,-35),(,,y,,=,-8):}
y-9z=-35" "implies" "(-8)-9z=-35" "implies" "z=3
x-7y+8z=85" "implies" "x-7(-8)+8(3)=85" "implies" "x=5
(5,-8,3)
Find the standard form of the equation of the ellipse with foci (0,2) and (0,-2) and vertices (0,4) and (0,-4).
a^2=b^2+c^2" "implies" "16=b^2+4" "implies" "b^2=12
x^2/12+y^2/16=1