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# The Circle

### All about circles...

Question | Answer |
---|---|

------derive their name because each ------ is the intersection of a right circular cone and a plane. | Conic sections |

What is the set of all points in a plane that are the same distance from a fixed point called the center? | A circle |

In this standard form equation, what is the center and what is the radius? (x-h)²+(y-k)²=r² | Center (h,k) Radius r |

The midpoint of the diameter of a circle is always the...? | Center |

What is the center and radius? (x+1)²+y²=8 | Center (-1,0) Radius 2 sq.root 2 or about 2.8 |

Twice a circle's radius is its...? | Diameter |

Find an equation of the circle with center (-7,3) and radius 10. | Standard form: (x-h)²+(y-k)²=r² --> (x-(-7))²+(y-3)²=10² --> (x+7)²+(y-3)²=100 |

Is x=y²-1 a circle or a parabola? If this is a parabola, what direction does it open? | Parabola, that opens to the right, because equations of circles always have both x² and y² and parabolas have only one or the other. It opens to the right because a=1 which is greater than 0, so the parabola opens to the right. |

x²+y²+2x-6y=39 Is this a circle or a parabola? | Circle. Center (-1,3), Radius 7. How to: (x²+2x)+(y²-6y)=39 (x²+2x+1)+(y²-6y)=39+1 (x²+2x+1)+(y²-6y+9)=39+1+9 (x+1)²+(y-3)²=49 h=-1,k=3,r=7 |

Is x=-2y² a circle or a parabola? If this is a parabola, what direction does it open? | Parabola, that opens to the left, because a=-2, a is less than 0, so it will open to the left. |

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