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.