1. Translate and Classify Conics
I.. Translating Conics (from Standard Form Equations).
A) Parabolas: no change. The Vertex is the translation.
B) Circles: (x – h)2 + (y – k)2 = r2
C) Ellipses:
D) Hyperbolas: or
E) The translation “slides” the center to (h , k)
1) Set the inside = 0 & solve. (change the sign)

2. Translate and Classify Conics
II. What is Classifying Conics.
A) Classifying means identifying which conic you have from an equation that is NOT written in standard form.
B) The equations we will be asked to classify will be written in
ax2 + by2 + cx + dy + e = 0 form.
1) Sometimes, the terms will be jumbled around.
2) Move terms around until they are in the above form.
C) Each type of Conic has parts of its equation that make it unique from all the others. We must find those parts.
1) We will find the uniqueness of the standard form eq.
2) Then we will “convert” that into the non-standard eq.

3. Translate and Classify Conics
III. Uniqueness of Parabolas.
A) Parabolas:
1) Standard form: y = ax2 + bx + c or x = ay2 + by + c
2) Uniqueness: one term squared, the other is not.
B) Classifying parabolas.
1) Look to see if only one term is squared.
a) Circle the x2 & y2 terms.
You will only be able to draw ONE circle.

4. Translate and Classify Conics
IV. Uniqueness of Circles.
A) Circles:
1) Standard form: x2 + y2 = #
2) Uniqueness: height & width are the same.
B) Classifying circles.
1) Both terms are squared, and have the same #.
a) Circle the x2 & y2 terms.
The numbers in front of the terms are the same.

5. Translate and Classify Conics
V. Uniqueness of Ellipses.
A) Ellipses:
1) Standard form:
2) Uniqueness: height & width are different.
B) Classifying ellipses.
1) Both terms are squared, but have different #s.
a) Circle the x2 & y2 terms.
The numbers in front of the terms different.
They are both positive (or both negative).

6. Translate and Classify Conics
VI. Uniqueness of Hyperbolas.
A) Hyperbolas:
1) Standard form: or
2) Uniqueness: one is positive & the other is negative.
B) Classifying hyperbolas.
1) Both terms are squared, but have different signs.
a) Circle the x2 & y2 terms.
The signs are different.