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|
|Foreign Language||Arabic Subtitled|
|Functions||Interpret expressions for functions in terms of the situation they model|
Translate between the geometric description and equation for a conic section
|Product Type||ACT Math|
|Properties, Measurement, and Dimension||Translate between the geometric description and the equation for a conic section|
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.