Conics Formulas Flashcards

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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?

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

What is the focus for a horizontal parabola?

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

What is the directrix for a vertical parabola?

<p>y = k - p</p> Signup and view all the answers

What is the directrix for a horizontal parabola?

<p>x = h - p</p> Signup and view all the answers

What is the axis of symmetry for a vertical parabola?

<p>x = h</p> Signup and view all the answers

What is the axis of symmetry for a horizontal parabola?

<p>y = k</p> Signup and view all the answers

What is the value of a?

<p>1/4p</p> Signup and view all the answers

What is the value of p?

<p>1/4a</p> Signup and view all the answers

What is the formula for a vertical ellipse?

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

What is the formula for a horizontal ellipse?

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

What is the center of an ellipse?

<p>(h,k)</p> Signup and view all the answers

What are the foci of a vertical ellipse?

<p>(h,k+c),(h,k-c)</p> Signup and view all the answers

What are the foci of a horizontal ellipse?

<p>(h+c,k),(h-c,k)</p> Signup and view all the answers

What are the vertices of a vertical ellipse?

<p>(h,k+-a)</p> Signup and view all the answers

What are the vertices of a horizontal ellipse?

<p>(h+-a,k)</p> Signup and view all the answers

What is the length of the major axis?

<p>2a</p> Signup and view all the answers

What is the length of the minor axis?

<p>2b</p> Signup and view all the answers

How to find c for an ellipse?

<p>c^2=a^2-b^2</p> Signup and view all the answers

What is the formula for a horizontal hyperbola?

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

What is the formula for a vertical hyperbola?

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

What are the foci of a vertical hyperbola?

<p>(h, k+c), (h, k-c)</p> Signup and view all the answers

What are the foci of a horizontal hyperbola?

<p>(h+c, k), (h-c, k)</p> Signup and view all the answers

What are the asymptotes of a horizontal hyperbola?

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

What are the asymptotes of a vertical hyperbola?

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

How to find c for a hyperbola?

<p>c^2=a^2+b^2</p> Signup and view all the answers

What is the equation of a circle?

<p>(x - h)^2+(y - k)^2=r^2 (A)</p> Signup and view all the answers

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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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