Standard form for conics
Presentation
•
Mathematics
•
10th Grade - University
•
Practice Problem
•
Medium
Standards-aligned
Amy Latsch
Used 37+ times
FREE Resource
7 Slides • 12 Questions
1
Standard form for conics
2
Open Ended
Give me your best guess about how you can tell the difference between the equations of a circle and an ellipse.
3
Open Ended
Give me your best guess about how you can tell the difference between the equations of an ellipse and a hyperbola.
4
Open Ended
Give me your best guess about how you can tell an equation is a parabola.
5
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
6
Multiple Choice
Which type of conic is:
137 + 6y = -3y2 - 3x2 + 24x
Circle
Ellipse
Hyperbola
Parabola
7
Multiple Choice
Which type of conic is:
137 + 6y = 3y2 - 3x2 + 24x
Circle
Ellipse
Hyperbola
Parabola
8
Multiple Choice
BE CAREFUL
Which type of conic is:
137 + 6y - 3y2 = - 3x2 + 24x
Circle
Ellipse
Hyperbola
Parabola
9
Multiple Choice
Which type of conic is:
137 + 6y = 3y2 + 6x2 + 24x
Circle
Ellipse
Hyperbola
Parabola
10
Multiple Choice
Which type of conic is:
137 + 6y = 3y2 + 24x
Circle
Ellipse
Hyperbola
Parabola
11
Multiple Choice
Which type of conic is:
Circle
Ellipse
Hyperbola
Parabola
12
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
13
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
14
How'd you do it?
x2 + y2 - 6x + 8y - 11 = 0
15
Now we will do it with something a little different:
3x2 + y2 - 6x + 8y - 11 = 0
16
Now we will do it with something a little different:
y2 - 3x2 - 6x + 8y - 11 = 0
17
Now we will do it with something a little different:
3y2 - x + 12y - 11 = 0
18
Poll
Can you tell the difference between the equations?
Yes
No
Kinda
19
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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Standard form for conics
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