Conics 2.1 Lecture

Conics 2 Lecture

Ellipse and Hyperbola​

By Elo Cheng

-the set of all points (x,y) in a plane the sum of whose distances from two distinct fixed points (foci is constant.

Ellipse

-The line through the foci intersects the ellipse at two points called VERTICES

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-The chord joining the vertices is the MAJOR AXIS, and its midpoint is the CENTER​ of the ellipse.

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-The chord perpendicular to the major axis through the center is the MINOR AXIS.​

Ellipse

The standard form of the equation of an ellipse, with center (h,k) and major and minor axes of lengths 2a and 2b, respectively, where 0<b<a, is

Standard Equation of an Ellipse

If the center is at the origin (0,0), the equation takes one of the following forms:

Multiple Choice

Which is a horizontal ellipse?

• $$\frac{x^2}{4}+\frac{y^2}{9}=1$$

• $$\frac{x^2}{16}+\frac{y^2}{9}=1$$

• $$\frac{x^2}{16}+\frac{y^2}{16}=1$$

• $$x^2+\frac{y^2}{49}=1$$

Multiple Choice

The midpoint of the line segment connecting the foci is the _____.

• co-vertice

• major axis

• center

• minor axis

Identify the center, vertices, co-vertices, and foci of the following ellipse.

Identify the center, vertices, co-vertices, and foci of the following ellipse.

Multiple Choice

What are the vertices of

$$\frac{x^2}{16}+\frac{y^2}{25}=1?$$  

• $$\left(-4,\ 0\right)\ and\ \left(4,\ 0\right)$$  

• $$\left(0,\ -4\right)\ and\ \left(0,\ 4\right)$$  

• $$\left(-5,\ 0\right)\ and\ \left(5,\ 0\right)$$  

• $$\left(0,\ -5\right)\ and\ \left(0,\ 5\right)$$  

Fill in the Blanks

How long is the major axis of the given ellipse?

$\frac{x^2}{64}+\frac{\left(y+2\right)^2}{49}=1$  

Fill in the Blanks

What is the center of the given ellipse? 

$\frac{\left(x+5\right)^2}{64}+\frac{\left(y-8\right)^2}{4}=1$  

Sketch the graph of the ellipse described by the following equation:

Sketch the graph of the ellipse described by the following equation:

Multiple Choice

Which of the following is the graph of  $$\frac{\left(x+3\right)^2}{4}+\frac{\left(y+1\right)^2}{9}=1$$  

Draw

Sketch the graph of the ellipse described by the following equation:

$$9x^2+4y^2-36x+24y+36=0$$  

Use the information below to write the standard form equation of the ellipse:

Use the information below to write the standard form equation of the ellipse:

(-10,-2), (-10,-10)  Endpoints of Minor Axis

Multiple Choice

Find the standard equation of the given ellipse

Multiple Choice

Find the standard equation of the given ellipse

End of Slides