Identifying Conic Sections

Question 1

What is the Standard Form for the Circle?

Answer 1

(x-h)^2+(y-k)^2=r^2.

Question 2

What is the Standard Form for the Ellipse?

Answer 2

Horizontal Axis: (((x-h)^2)/a^2)+((y-k)^2)/b^2=1.

Vertical Axis: (((x-h)^2)/b^2)+((y-k)^2)/a^2=1.

Question 3

What is the Standard Form for the Hyperbola?

Answer 3

Horizontal Axis: (((x-h)^2)/a^2)-((y-k)^2)/b^2=1.

Vertical Axis: (((y-k)^2)/a^2)-((x-h)^2)/b^2=1.

Question 4

What is the Standard Form for the Parabola?

Answer 4

Horizontal Axis: x-h=(1/4p)((y-k)^2).

Vertical Axis: y-k=(1/4p)((x-h)^2).

Question 5

How do you find if an equation of the form Ax^2+Bxy+Cy^2+Ey+F=0 is a Circle?

Answer 5

B^2-4AC<0, B=0 and A=C.

Question 6

How do you find if an equation of the form Ax^2+Bxy+Cy^2+Ey+F=0 is a Ellipse?

Answer 6

B^2-4AC<0 and either B does not equal 0 or A does not equal C.

Question 7

How do you find if an equation of the form Ax^2+Bxy+Cy^2+Ey+F=0 is a Hyperbola?

Answer 7

B^2-4AC>0.

Question 8

How do you find if an equation of the form Ax^2+Bxy+Cy^2+Ey+F=0 is a Parabola?

Answer 8

B^2-4AC=0.

Question 9

How can you convert an Equation of a Conic from Standard Form to General Form?

Answer 9

By expanding the Binomials.

Question 10

How can you convert an Equation of a Conic Section from General Form to Standard Form?

Answer 10

By Completing the Square.