### Find all polar coordinates of point p = (6, 31°).

This question aims to find the polar coordinates of a point P that is equal to (6, 31°). P is a point on the xy plane. x and y axis are known as the polar axis, while the origin of the xy plane is called the pole. The point P is represented in the form […]

### Find the equation of the sphere centered at (-4, 1, 4) with radius 3. Give an equation which describes the intersection of this sphere with the plane z = 6.

This question aims to find the equation of the sphere centered at (-4, 1, 4) in 3D coordinates and also an equation to describe the intersection of this sphere with a plane z=6. The question is based on the concepts of a solid geometry. Solid geometry is the part of mathematics geometry that deals with solid […]

### 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: Read moreIdentify the surface whose equation is given. ρ=sinθsinØ[ dfrac{ y – […]

### 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 […]