# ACT Math 3.1 Coordinate Geometry

ACT Math: Coordinate Geometry Drill 3, Problem 1. What shape is shown by the equation in this video?

ACT Math | Coordinate Geometry |

ACT Mathematics | Coordinate Geometry |

Algebra | Coordinates and Graphs |

Coordinate Geometry | Conic sections Conics |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Functions | Interpret expressions for functions in terms of the situation they model |

Geometry | Coordinate Geometry Translate between the geometric description and equation for a conic section |

Language | English Language |

Precalculus | Conic Sections |

Product Type | ACT Math |

Properties, Measurement, and Dimension | Translate between the geometric description and the equation for a conic section |

### Transcript

First we can eliminate C, triangle from our options, because a

triangle cannot be shown by one equation

it's made up of three lines. Alright let's move back to A

Circle, the standard formula of a circle is

R-squared equals quantity X minus H squared plus quantity Y minus K

squared where R is the radius

HK is the center of the circle

The circle formula has X and Y radius to the second power

but our equation only raises one variable Y

to the second power. So we can cross A off our list.

Next up B. Ellipse, while the formula

of an ellipse is quantity X minus H square divided by

A squared plus quantity Y minus K squared

divided by B squared equals one where HK is the center

and A is half the length of the major axis

and B is half of the minor axis...well

does that look like our equation? No! Cross off B.

Next up, D, Parabola.

The equation of an up or down parabola

is Y minus K equals quanitiy

X minus H squared. Does that look like our equation? Well...

...Close but not quite, but wait what about those

sideways parabolas? Well the equation of a sideways parabola is

X minus H equals quantity Y minus K squared

and our equation is X minus 4 equals quanity Y plus 2 squared

Is that a match? Yeah! In our sideways parabola

H is 4 and K is negative 2. Got our answer.

D...Parabola