Polygons on the Coordinate Plane
Which triangle has angles that are all less than 90 degrees?
Acute.
What is the equation of a circle in a center-radius form?
(x-h)2 + (y-k)2 = r2
Find the vertex of the parabola.
Focus: (7,13) Directrix: y = 1
Vertex: (2,7)
Define: central angle, arc and sector.
A central angle is an angle formed at the center of a circle by two radii. An arc is a portion of the circle's circumference. A sector is a region of a circle enclosed by two radii and the arc between them, resembling a slice of pie
What is a tangent?
What is a chord?
A chord is a segment whose endpoints lie on a circle.
A tangent is a line that touches the circle at exactly one point and is perpendicular to the radius at that point.
What is the slope formula?
m = (y₂ - y₁) / (x₂ - x₁)
Write the equation of a circle with a center (2,4) and a radius of 2.
(x-2)2 + (y-4)2 = 22
Find the vertex, focus, and directrix of the parabola.
y-4=1/16(x-6)2
vertex:(6,4)
focus:(6,8)
directrix: y = 0
Find the measure of a major arc if the central angle is 120 degrees.
240 degrees.
Find the length of a tangent from a point 13 units from the center of a circle with a radius of 5.
12
What are all the different types of quadrilaterals?
Parallelogram
Rectangle
Square
Rhombus
Find the center and the radius from the equation:
(x-3)2 + (y+5)2 = 144
center is (3,-5) and the radius is 12.
Find the vertex, focus, and directrix of the parabola.
y+7=1/12(x-4)2
V:(4,-7)
F:(4,-4)
D: y = -10
Find the arc length of a circle with a radius of 6 and an arc measure of 60 degrees.
2pi
Find the measure of an inscribed angle that intercepts a 100 degrees arc.
50 degrees
What formula should you use when trying to find the distance between two points? Also show the formula.
Distance formula.
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the equation of the circle, find the radius and center. (x+7)2 + (y-2)2 = 16
radius:4
center:(-7,2)
Write an equation of the parabola with the given focus and vertex.
focus:(5,10)
vertex: (5,5)
y-5=1/25(x-5)2
Find the area of a sector with a radius of 20 and a central angle of 90 degrees
100pi square units
Two chords intersect inside a circle. If one chord is split into parts 4 and 6 and the other parts x and 3, solve for x.
8 = x
Find the distance between all the vertices. A(1,2), B(-3,-5), C(1,6).
AB: √33
BC:√137
AC:4
Center:(2,-3) Point on Circle:(5,-3) Write an equation of then circle in center radius form.
(x-2)2 + (y+3)2 = 32
Write and equation of each parabola with the given focus and vertex.
focus:(-6,4)
vertex:(-6,2)
y-2=1/4(x+6)2
A circle has a circumference of 10pi. Find the arc length of a 135 degree arc.
3.75pi square units
In triangle inscribed in a circle, angle E = 40 degrees and angle F = 50 degrees. Find the measure of arc DF.
90 degrees