When students hear about the Cartesian equation they get terrified by the word itself and get

anxious. This is the equation that is used in mathematics and the students who study math’s are

supposed to write assignments on this equation at least one time.

Before understanding the effective guidelines of the cartesian equation first let us understand

**What is Cartesian Equation.**

Cartesian Equation is an equation of a surface or a curve where variables present as a coordinate

on a surface or curve on a reference of a point. The example of a Cartesian equation can be

ax+by+cz = d, where d is considered as the distance and c, b, a is considered as the direction

from the origin of a plane. Rene Descartes discovered this equation in the 17th century. This

equation is the combination or link between geometry and algebra. In Cartesian Equation there

are two coordinates, and they are, the x coordinate and the y coordinate. And these coordinates

can be defined as the perpendicular lines on both the x-axis and y-axis.

How To Convert The Equation From Polar Equation To Cartesian Equation

**In Four To Five Simple Steps?**

Polar Equation is the equation that defines the relation between the angle and the distance of a

point from the curve (the relation between theta and r r r where theta is the angle and r r r is the

distance). There are several steps with the help of which it is possible to convert a Polar Equation

into a Cartesian Equation.

Conversion of Cartesian to Polar

Y=rsinθ

X= rcosθ

Conversion of Polar to Cartesian

r2 = x2+ y2

tanθ=y/x

**Step 1 Identification of the type of the equation**

When we look at the equation it is not difficult to understand the form of the equation. It is said

to be in cartesian form when it incorporates xs and ys ad it is said to be in polar form when it

incorporates θs and rs.

**Step 2 Stating the objective**

If there is a equation that is in the Cartesian form then the aim should be to convert it in a way that we

left with only θs and rs and if the equation is in the polar form then the goal should be to convert it in a

way that we left with only ys and xs. If these points are there in the mind then it would be easy to

solve the equation and not get stuck in between.

**Step 3 Examine the equation**

Some key points are to be noted in the equation and the equation should be examined.

**Step 4 Substitution**

By keeping step 2 in the mind, substitution should be done.

5r2= rsin (θ)

5 (x2+y2)= y

**Step 5 Squares completion and Combining like-terms**

Terms should be combined and squares should be completed where required while simplifying

the equation. There are three equations below where some mathematician asks to bring the right-

hand side zero. While some will ask to do the factor of the term. These three equations can be

simplified as:

5 (x2+y2) = y

5×2+ 5y2-y =0

5×2+y (5y-1)= 0

As these are the five steps with the help of which we are now able to convert the equation from a

Polar equation to a Cartesian Equation. If you still find it hard to convert it Moodle monkey

website makes it easy to understand.

**How To Convert The Equation From Parametric Equation To Cartesian**

**Equation?**

A parametric equation is an equation where a group of quantities that are present with one or

more than one variable is said to be parameters. Now let us understand the conversion process

from the Parametric to the Cartesian equation.

Now,

x=e4t, y= t+9

**Steps that are considered**

1. If we have to find the Cartesian Equation of the curve, the parameter should be eliminated.

2. With the help of an arrow the curve is traced and sketched later.

Procedure

Step1 Now, we have x= e4t,

Now we have to eliminate the t and solve the equation.

Y= t+9

y-9=t

x= e 4(y-9)

Y=t+9

X= e4t

If we take the log on both sides and divide it by 4 on both sides,

lnx= 4t

Lnx/4= t

Put it back in the y equation

y=ln(x)/4 +9

Now both the equations are the desired equations which are in cartesian form and are correct as

well. Usually, the equation which is equal to Y is generally accepted more. We can write the

equations normally like.

y= mx+b

Step 2 Now the curve is sketched where the parameter is increased and then later table is made

using x,y, and t as variables

T- 0 1 2 3 4

X -1 4 8 12 16

Y- 9 10 11 12 13

Where t is independent and others are the dependent variables such as x and y.

Moodle monkey is a website that provides easy explanations and easy steps to understanding the

methods of Cartesian Equations and the conversion of Cartesian Equations.