Conic Section Formulas

Question 1

What is an ellipse’s standard form and attributes?

Answer 1

(X-h)^2 /a^2 + (y-k)^2 /b^2 = 1

Center: (h,k)
Vertices: (h+-a,k) , (h, k+-b)

Question 2

What is a parabola’s standard form and attributes (quadratic x)

Answer 2

Y= (x-h)^2 /4c + k

Vertex: (h,k)
C>0, opens up
C<0, opens down

Question 3

What is a parabola’s standard form and attributes? (Quadratic y)

Answer 3

X= (y-k)^2 /4c + h

Vertex: (h,k)
C>0, opens right
C<0, opens left

Question 4

What is a hyperbola’s standard form and attributes? (Y leading)

Answer 4

(Y-k)^2 /a^2 - (x-h)^2 /b^2 =1

Opens up and down
Center: (h,k)
Vertices: (h, k+-a)

Question 5

What is a hyperbola’s standard form and attributes? (x leading)

Answer 5

(X-h)^2 /a^2 - (y-k)^2 /b^2 =1

Opens left and right
Center: (h,k)
Vertices: (h+-a, k)