Finding the Square or Rectangle Area Given Four Points
Given four points in the Cartesian plane, A(2,2), B(5,2), C(5,6), and D(2,6), what is the area of the rectangle formed by these points?
Finding the Square or Rectangle Perimeter Given Four Points
Given four points A(1,3), B(4,3), C(4,1) and D(1,1) in a two-dimensional plane, what is the perimeter of the rectangle formed by these points?
Finding the Square or Rectangle Area Given Three Points
In the cartesian coordinate system, three points A(0,0), B(6,0), and C(0,4) are given. What is the area of the rectangle formed by these three points?
Finding the Square or Rectangle Perimeter Given Three Points
Given three points A(1, 3), B(1, 1), and C(4, 1) on a plane, which are the vertices of a rectangle, find the perimeter of the rectangle.
Finding the Equation of a Circle
The signal of Micha's Wi-Fi router covers a circular area, whose border is modeled by the equation $(x-7)^{2}+y^{2}=r^{2}$. She discovers the boundary is located at $(4,4)$. What is the radius of the signal?
5
$\sqrt{32}$
25
32
Finding the Equation of a Hyperbola
Given the foci of a hyperbola are at (0, 5) and (0, -5), and the distance from the center to one vertex is 4, find the equation of the hyperbola.
Finding the Equation of an Ellipse
Find the equation of the ellipse that has its center at the origin (0,0), semi-major axis a=4 and semi-minor axis b=3.