Standard form for conics

Standard form for conics

Open Ended

Give me your best guess about how you can tell the difference between the equations of a circle and an ellipse.

Open Ended

Give me your best guess about how you can tell the difference between the equations of an ellipse and a hyperbola.

Open Ended

Give me your best guess about how you can tell an equation is a parabola.

Telling Conic Equations apart

• Circles have both x² and y² and their coefficients are the same when equation is set = 0

• Ellipses have both x² and y² and their coefficients are different, but have the same sign when equation is set = 0

• Hyperbolas have both x² and y² and their coefficients have opposite signs when equation is set = 0

• Parabolas have only one variable being squared

Multiple Choice

Which type of conic is:

137 + 6y = -3y² - 3x² + 24x

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

Which type of conic is:

137 + 6y = 3y² - 3x² + 24x

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

BE CAREFUL

Which type of conic is:

137 + 6y - 3y² = - 3x² + 24x

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

Which type of conic is:

137 + 6y = 3y² + 6x² + 24x

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

Which type of conic is:

137 + 6y = 3y² + 24x

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

Which type of conic is:

• Circle

• Ellipse

• Hyperbola

• Parabola

How do we go from standard form to center form?

• Put ALL the variables on 1 side and the constant on the other

• Group like terms together

• Factor any coefficients of the square terms forward

• Do what we did with circles

Multiple Choice

Put

x² + y² - 6x + 8y - 11 = 0 into center form.

• (x - 3)² + (y + 4)² = 11

• (x - 3)² + (y + 4)² = -14

• (x - 3)² + (y + 4)² = 36

• (x - 3)² + (y + 4)² = 18

How'd you do it?

x² + y² - 6x + 8y - 11 = 0

Now we will do it with something a little different:

3x² + y² - 6x + 8y - 11 = 0

Now we will do it with something a little different:

y² - 3x² - 6x + 8y - 11 = 0

Now we will do it with something a little different:

3y² - x + 12y - 11 = 0

Poll

Can you tell the difference between the equations?

• Yes

• No

• Kinda

Poll

1 - Not at all

5 - Definitely got it

How's putting the equations into center form coming along? Be honest, we will do more!

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