WRITING EQUATIONS OF CONICS IN VERTEX FORM MM

WRITING EQUATIONS OF CONICS IN VERTEX FORM MM 3 G 2

Write the equation for the circle in vertex form:

Example 1

Example 1

Example 1

Example 1

Write the equation for the circle in vertex form:

Example 2

Example 2

Example 2

Example 2

Write the equation for the circle in vertex form:

Example 3

Example 3

Example 3

Example 3

Write the equation for the circle in vertex form:

Example 4

Example 4

Example 4

Example 4

Recall: The equation for a circle does not have denominators The equation for an ellipse and a hyperbola do have denominators The equation for a circle is not equal to one The equation for an ellipse and a hyperbola are equal to one We have a different set of steps for converting ellipses and hyperbolas to the vertex form:

Write the equation for the ellipse in vertex form:

Example 5

Example 5

Example 5

Example 5

Example 5 9 4 1

What is the center of this ellipse? What is the length of the major axis? What is the length of the minor axis?

Example 6: Ellipse Step 1: Step 2: Step 3:

Example 6 Step 4: Step 5:

Example 6 Step 6: 25 4 1

What is the center of this ellipse? What is the length of the major axis? What is the length of the minor axis?

Example 7: Ellipse Step 1: Step 2: Step 3:

Example 7 Step 4: Step 5:

Example 7 Step 6: 36 81 1

What is the center of this ellipse? What is the length of the major axis? What is the length of the minor axis?

Example 8: Hyperbola Step 1: Step 2: Step 3:

Example 8 Step 4: Step 6:

Example 8 Step 6: 2 1

What is the center of this hyperbola? What is the length of the transverse axis? What is the length of the conjugate axis?

Example 9: Hyperbola Step 1: Step 2: Step 3:

Example 9 Step 4: Step 5:

Example 9 Step 6: 9 1 4

What is the center of this hyperbola? What is the length of the transverse axis? What is the length of the conjugate axis?

You Try!