Conics Formulas Flashcards

Questions and Answers

What is the formula for a vertical parabola?

y=a(x-h)^2 + k (correct)

x = a(y-k)^2 + h

y = k - p

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

What is the formula for a horizontal parabola?

y=a(x-h)^2 + k

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

y = k - p

x = a(y-k)^2 + h (correct)

What is the vertex of a parabola?

(h,k)

What is the focus for a vertical parabola?

(h,k+p) Signup and view all the answers

What is the focus for a horizontal parabola?

(h+p,k) Signup and view all the answers

What is the directrix for a vertical parabola?

y = k - p Signup and view all the answers

What is the directrix for a horizontal parabola?

x = h - p Signup and view all the answers

What is the axis of symmetry for a vertical parabola?

x = h Signup and view all the answers

What is the axis of symmetry for a horizontal parabola?

y = k Signup and view all the answers

What is the value of a?

1/4p Signup and view all the answers

What is the value of p?

1/4a Signup and view all the answers

What is the formula for a vertical ellipse?

(x-h)^2/a^2+(y-k)^2/b^2=1 Signup and view all the answers

What is the formula for a horizontal ellipse?

(x-h)^2/b^2+(y-k)^2/a^2=1 Signup and view all the answers

What is the center of an ellipse?

(h,k) Signup and view all the answers

What are the foci of a vertical ellipse?

(h,k+c),(h,k-c) Signup and view all the answers

What are the foci of a horizontal ellipse?

(h+c,k),(h-c,k) Signup and view all the answers

What are the vertices of a vertical ellipse?

(h,k+-a) Signup and view all the answers

What are the vertices of a horizontal ellipse?

(h+-a,k) Signup and view all the answers

What is the length of the major axis?

2a Signup and view all the answers

What is the length of the minor axis?

2b Signup and view all the answers

How to find c for an ellipse?

c^2=a^2-b^2 Signup and view all the answers

What is the formula for a horizontal hyperbola?

(x-h)^2/a^2-(y-k)^2/b^2=1 Signup and view all the answers

What is the formula for a vertical hyperbola?

(y-k)^2/a^2-(x-h)^2/b^2=1 Signup and view all the answers

What are the foci of a vertical hyperbola?

(h, k+c), (h, k-c) Signup and view all the answers

What are the foci of a horizontal hyperbola?

(h+c, k), (h-c, k) Signup and view all the answers

What are the asymptotes of a horizontal hyperbola?

y = k +/- b/a (x-h) Signup and view all the answers

What are the asymptotes of a vertical hyperbola?

y = k +/- a/b (x-h) Signup and view all the answers

How to find c for a hyperbola?

c^2=a^2+b^2 Signup and view all the answers

What is the equation of a circle?

(x - h)^2+(y - k)^2=r^2 Signup and view all the answers

Study Notes

Parabolas

Vertical Parabola Formula: ( y = a(x - h)^2 + k )
Horizontal Parabola Formula: ( x = a(y - k)^2 + h )
Vertex of a Parabola: Given by the point ( (h, k) )
Focus for Vertical Parabola: Located at ( (h, k + p) )
Focus for Horizontal Parabola: Found at ( (h + p, k) )
Directrix for Vertical Parabola: Defined by the line ( y = k - p )
Directrix for Horizontal Parabola: Given by the line ( x = h - p )
Axis of Symmetry for Vertical Parabola: The line ( x = h )
Axis of Symmetry for Horizontal Parabola: The line ( y = k )
Relation between ( a ) and ( p ): ( a = \frac{1}{4p} )
Finding ( p ): ( p = \frac{1}{4a} )

Ellipses

Vertical Ellipse Formula: ( \frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1 )
Horizontal Ellipse Formula: ( \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1 )
Center of an Ellipse: Identified at the point ( (h, k) )
Foci of a Vertical Ellipse: Located at ( (h, k + c), (h, k - c) )
Foci of a Horizontal Ellipse: Positioned at ( (h + c, k), (h - c, k) )
Vertices of a Vertical Ellipse: Found at ( (h, k \pm a) )
Vertices of a Horizontal Ellipse: Located at ( (h \pm a, k) )
Length of Major Axis: Calculated as ( 2a )
Length of Minor Axis: Calculated as ( 2b )
Finding ( c ) for Ellipse: Use the equation ( c^2 = a^2 - b^2 )

Hyperbolas

Horizontal Hyperbola Formula: ( \frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1 )
Vertical Hyperbola Formula: ( \frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1 )
Foci of a Vertical Hyperbola: Positioned at ( (h, k + c), (h, k - c) )
Foci of a Horizontal Hyperbola: Located at ( (h + c, k), (h - c, k) )
Asymptotes of Horizontal Hyperbola: Given by the equations ( y = k \pm \frac{b}{a}(x - h) )
Asymptotes of Vertical Hyperbola: Given by the equations ( y = k \pm \frac{a}{b}(x - h) )
Finding ( c ) for Hyperbola: Calculated using ( c^2 = a^2 + b^2 )

Circle

Equation of a Circle: Given by ( (x - h)^2 + (y - k)^2 = r^2 ) where ( (h, k) ) is the center and ( r ) is the radius.

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Description

Test your knowledge of conic section formulas with these flashcards. Learn about the equations for vertical and horizontal parabolas, as well as key components such as vertices and foci. Perfect for students studying conics in mathematics.