Distance Formula
Midpoint Formula
Applications of Distance and Midpoint Formulas
Intro to Conic Sections
Parabolas
100
Find the distance between (5,8) and (-3, 8)
8
100
Find the midpoint of the line segment joining (2,6) and (2,12)
(2, 9)
100
Which points are farther apart from each other: (3,6) and (5,8) or (4,7) and (5,10)?
(4,7) and (5,10)
100
If you cut a cone parallel to its base, which conic section results?
A circle
100
Which direction does the graph of the equation y^2=4px open? (left, right, up, or down)
right
200
Find the distance between (0,3) and (3, 7)
5
200
Find the midpoint of the line segment joining (0,5) and (2,11)
(1,8)
200
Find the distance between the midpoint of the line segment joining (2,5) and (4,7) and the midpoint of the line segment joining (3,9) and (7,1).
square root of 5, or ~2.24
200
If you cut a conic section diagonally across its base, which conic section results?
An ellipse
200
What is the focus of the parabola whose equation is x^2=20y?
(0,5)
300
Find the distance between (2,6) and (7, 18)
13
300
Find the midpoint of the line segment joining (4,9) and (7,4)
(5.5,6.5)
300
Classify the triangle whose vertices are (1,4), (4,1), and (7,4) as scalene, isosceles, or equilateral.
Isosceles
300
If you cut a cone parallel to the slant of the outside edge, which conic section results?
A parabola
300
What is the directrix of the parabola whose equation is y^2=8x?
x = -2
400
Find the distance between (-3, 8) and (5, 12)
square root of 80, 4(square root of 5), or ~8.94
400
Find the midpoint of the line segment joining (-2,8) and (-8,-2)
(-5,3)
400
Classify the triangle with vertices (-4,3), (2,-1), and (8,-1) as scalene, isosceles, or equilateral.
scalene
400
If you cut a double-napped cone perpendicular to its base, which conic section results?
A hyperbola
400
What is the directrix of the parabola whose equation is x=4y^2
x = -1/16
500
Find the distance between (-4,7) and (3,-5)
square root of 193, or ~13.89
500
Find the midpoint of the line segment joining (-6,12) and (7,-5)
(.5,3.5)
500
If the distance between the points (-3,-1) and (2,y) is the square root of 41, determine the two possible values of y.
-5 and 3
500
Which conic section if defined as all the points equidistant from a point and a line?
A parabola
500
Find the focus of the parabola whose equation is -24x=3y^2
(-2,0)
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