 ### Find the point on the hyperbola xy = 8 that is closest to the point (3,0).

To solve this question, we have to determine the point on the hyperbola xy = 8 that is closest to the point (3,0). A hyperbola is defined as a conic section that is produced by the intersection of a plane and circular cone at any given angle so that halves of the circular cone are […]

### Line AB contains points A(4, 5) and B(9, 7). What is the slope of line AB?

The aim of this question is to understand and apply different forms of line. It also covers different parameters used in the linear equations such as slope and intercepts. According to two point form, an equation can be written in the following form: [ dfrac{ y – y_{ 1 } }{ y_{ 2 } – […]

### Find a Cartesian equation for the curve and identify it.

This problem aims to find the cartesian equation for the curve and after that identify the curve. To better understand the problem, you should be familiar with cartesian coordinate systems, polar coordinates, and conversion from polar to cartesian coordinates. A two-dimensional coordinate system in which a point on a plane is determined by a distance […]

### Find the coordinates of the vertex for the parabola defined by the given quadratic function.

[ boldsymbol{ f ( x ) = 2 x^{ 2 } – 8 x + 3 } ] The aim of this question is to learn how to evaluate the vertex location of a parabola. A U-shaped curve that follows the quadratic law (its equation is quadratic), is called a parabola. A parabola has a […]

### How many square feet is Rhode island?

The aim of this question is to learn unit conversions between different customary units in use in the United States of America. Rhode Island is the smallest state out of all the states within mainland of the United States of America. Its area is 776,960 acres. Although the international unit of area is square meters, there […]