Chapter 10 warm ups and instructions
10.1 warm ups and instructions
10.1 warm up
Write an equation for the perpendicular
bisector of the line segment joining (3, -7) and
(-3, 1).
10.2 warm ups and instructions
Conic sections - YouTube
http://rowdy.mscd.edu/~talmanl/MOOVs/Par
abolaDF/ParabolaDF_NS.mov
Construct a Parabola
10.2 warm up #1
Identify the focus and directrix of the
parabola.
1. 𝟑𝒚𝟐 = 𝒙
2. 𝒚𝟐 = 𝟐𝟎𝒙
3. 𝟒𝒙𝟐 = −𝒚
10.2 warm up #2
Graph the equation. Identify the focus,
directrix, and axis of symmetry of the
parabola.
1. 𝒙𝟐 = −𝟏𝟐𝒚
2. 𝒚𝟐 = 𝟖𝒙
3. 𝒙 +
𝟏 𝟐
𝒚
𝟏𝟐
=𝟎
10.2 warm up #3
Write the standard form of the equation of the
parabola with the vertex at (0, 0) and the
given focus or directrix.
1. Focus: (0, 3)
2. Focus: (
−𝟑
, 𝟎)
𝟐
3. Directrix: 𝒚 = −𝟑
4. Directrix: 𝒙 = 𝟒
10.3 warm ups and instructions
Circle
10.3 warm up
1. Graph the equation. Identify the radius of
the circle.
a) 𝒙𝟐 + 𝒚𝟐 = 𝟕
b) 𝒙𝟐 = 𝟒𝟎𝟎 − 𝒚𝟐
c) 𝟏𝟔𝒙𝟐 + 𝟏𝟔𝒚𝟐 = 𝟑𝟐
2. Write the standard form of the equation of
the circle with the given radius and center at
(0, 0).
a. 10
b. √𝟏𝟏
c. 𝟑√𝟐
3. Write the standard form of the equation of
the circle that passes through the given point
and whose center is at the origin.
(-4, -1)
5. The equation of a circle and a point on the
circle is given. Write an equation of the line
that is tangent to the circle at that point.
𝒙𝟐 + 𝒚𝟐 = 𝟒𝟏; (−𝟒, −𝟓)
10.4 warm ups and instructions
Definition
Ellipse – the set of all points P such that the
sum of the distances between P and two
distinct fixed points, called the foci, is a
constant.
Tracing An Ellipse (Sum-of-The-Distances
Definition)
Characteristics and equations (see page 609)
Equation of an Ellipse in standard form and
how it relates to the graph of the Ellipse.
10.4 warm up #1
Problems from the above web site
10.4 warm up #2
Write the equation in standard form. Then
identify the vertices, co-vertices, and foci of
the ellipse.
1. 𝟗𝒙𝟐 + 𝟏𝟔𝒚𝟐 = 𝟏𝟒𝟒
2. 𝟐𝟓𝒙𝟐 + 𝟒𝟗𝒚𝟐 = 𝟏𝟐𝟐𝟓
Graph the equation. Identify the vertices, covertices and foci ON YOUR GRAPH.
3. 𝟗𝒙𝟐 + 𝟒𝒚𝟐 = 𝟑𝟔
Write an equation of the ellipse with the given
characteristics and center at (0, 0).
4. vertex: (𝟗, 𝟎), focus: (𝟒√𝟐, 𝟎)
5. co-vertex: (𝟒, 𝟎), focus: (𝟎, 𝟑)
Review bullet points for the 10.1 – 10.4 quiz
 definitions: circle, distance formula,
ellipse, midpoint formula, parabola
 finding the distance between two points,
the midpoint of two points, and the
equation of the perpendicular bisector of a
segment given the endpoints of the
segment
 finding the standard form of an equation
of a conic section given information about
it or a non-standard form of its equation
 graphing conic sections
 word problems involving conic sections
10.5 Warm ups and instructions
Definition
Hyperbola – the set of all points P such that
the difference of the distances from P to two
fixed points, called the foci, is constant.
Difference of distances illustration of a
hyperbola
Tracing A Hyperbola (Difference-of-TheDistances Definition)
Equations of a hyperbola with center at the
origin
Formula and graph of a hyperbola. How to
graph a hyperbola based on its formula
10.5 Warm up
Write the equation of the hyberbola in
standard form, if necessary. Then identify the
foci and vertices of the hyperbola
1.
𝒚𝟐
𝟔𝟒
−
𝒙𝟐
𝟐𝟓
=𝟏
2. 𝟐𝟓𝒙𝟐 − 𝟏𝟔𝒚𝟐 = 𝟒𝟎𝟎
3. 𝒚𝟐 − 𝟏𝟔𝒙𝟐 − 𝟏𝟔 = 𝟎
4. Write an equation of the hyperbola with
the given foci and vertices.
Foci: (±𝟒, 𝟎)
Vertices: (±𝟏, 𝟎)
10.6 Warm ups and instructions
Definition
Conic section – a curve formed by the
intersection of a plane and a double-napped
cone.
10.6 Warm up #1
Write an equation for the conic section.
1. Circle with center at (-3, 1) and radius 5
2. Ellipse with vertices at (-9, 3) and (1, 3)
and foci at (-7, 3) and (-1, 3)
3. Parabola with vertex at (-4, -3) and focus
at (1, -3)
10.6 Warm up #2
Graph the equation. Identify the important
characteristics of the graph, such as center,
vertices, and foci.
1.
𝒙𝟐
𝟔𝟒
−
(𝒚−𝟑)𝟐
𝟗
=𝟏
2. 𝟑(𝒙 + 𝟒)𝟐 + 𝟑(𝒚 + 𝟏)𝟐 = 𝟒𝟖
10.6 Warm up #3
Classify the conic section and write its
equation in standard form.
1. 𝟓𝒙𝟐 + 𝟓𝒚𝟐 + 𝟏𝟎𝒙 − 𝟐𝟎𝒚 − 𝟐𝟎 = 𝟎
2. 𝒙𝟐 − 𝟒𝒙 + 𝟐𝟎𝒚 − 𝟏𝟔 = 𝟎
3. 𝒙𝟐 + 𝟏𝟔𝒚𝟐 − 𝟒𝒙 + 𝟏𝟐𝟖𝒚 + 𝟐𝟓𝟔 = 𝟎
10.7 Warm ups and instructions
Solving nonlinear systems
Solve either by substitution or by the
elimination method
1 – 4 Solve the system of equations
1. 𝒚 = 𝟏𝟐𝒙 − 𝟑𝟎; 𝟒𝒙𝟐 − 𝟑𝒚 = 𝟏𝟖
2. 𝟖𝒚 = −𝟏𝟎𝒙; 𝒚𝟐 = 𝟐𝒙𝟐 − 𝟕
3. 𝒙𝟐 + 𝒚𝟐 − 𝟖𝒚 + 𝟕 = 𝟎;
−𝒙𝟐 + 𝒚 − 𝟏 = 𝟎
4. 𝟏𝟎𝒙𝟐 − 𝟐𝟓𝒚𝟐 − 𝟏𝟎𝟎𝒙 = −𝟏𝟔𝟎
𝒚𝟐 − 𝟐𝒙 + 𝟏𝟔 = 𝟎
Review bullet points for the 10.5 – 10.7 quiz
 Definition: conic section
 Classifying conic sections from their
general form equations
 Finding standard form of conic equations
given the general form of their equations
 Graphing translated conic sections given
their equations in general form
 Solving systems of equations in which at
least one of the equations is non-linear
10.5 – 10.7 review warm up
a) Problems 12, 13 on page 645
b) Problems 24 – 35 on page 645 (classify
only, do not attempt to put in standard
form)
c) Problem 38 on page 645