Vectors
Given u = <3,-2> and v = <-1,5>, find the vector u + v
<2, 3>
Given x(t) = 3t + 1 and y(t)=t^2-2 find the coordinates of the point where t = 3
(10,7)
Find the vertex of the parabola
(y-3)^2=8(x+2)
(-2,3)
Find the center of the ellipse:
(x-5)^2/9 +(y+2)^2/25 = 1
(5,-2)
Does the hyperbola open up/down or left/right?
y^2/16 - x^2/9 = 1
Up/down (vertical transverse axis)
Given a = <4,1> and b = <-2,3> find 3a - 2b
<16, -3>
Eliminate the parameter to write the rectangular equation in terms of x and y:
x(t) =t-4 and y(t) = 2t+5
y = 2x + 13
State the direction that the parabola opens
(x+4)^2= -12(y-1)
Downward
Find the total length of the major axis for the ellipse:
y^2/49 +x^2/16=1
14
Find the center and the vertices of the hyperbola:
(x+1)^2/25 -(y-4)^2/16 = 1
Center (-1,4) and Vertices: (4,4) and (-6,4)
Find the dot product of u = <5,-4> and v = <2,3>
-2
Eliminate the parameter to write the rectangular equation and state the domain constraint for x.
x(t) = sqrtt and y(t) = 3t-1
y=3x^2 -1
x>=0
Find the coordinates of the focus for the parabola:
(x-1)^2=16(y+2)
(1,2)
Find the distance from the center to each focus for the ellipse:
x^2/100+y^2/64 = 1
c = 6
Find the asymptotes for the hyperbola:
y^2/36-x^2/49=1
y=+-6/7x
Find the angle between u = <3,4> and v = <5,12>
14.25 degrees
Find the AROC of y with respect to x for the parametric equations on the interval [1,3]:
x(t)=t^2 and y(t) = 3t
3/4
Write the standard form of the equation of a parabola with its vertex at (0,0) and a directrix of x = -5
y^2=20x
Write the standard form equation of an ellipse with its center at (0,0), a horizontal major axis length of 20, and a vertical minor axis length of 10.
x^2/100 + y^2/25=1
Find the coordinates of the foci for the hyperbola
x^2/64-y^2/36=1
(10,0) and (-10,0)
Find the unit vector in the opposite direction of v = <-6,8>
<3/5, -4/5>
Use Pythagorean Identity to eliminate the parameter and find the rectangular equation
x(t) = 4 cos(t) and y(t) = 4 sin(t)
x^2+y^2= 16
Complete the square to write the equation in standard form:
y^2-4y-4x+16=0
(y-2)^2=4(x-3)
Complete the square to write the ellipse equation in standard form:
4x^2+9y^2-24x+18y+9=0
(x-3)^2/9 +(y+1)^2/4 = 1
Complete the square to write the hyperbola equation in standard form:
9x^2-4y^2+54x+32y-19=0
(x+3)^2/4 -(y-4)^2/9 = 1