Ellipse is one of basis of mathematics.Ellipse is defined as the curve. The ellipse curve are having a locus of all point. In the rotated ellipse equation the distances are calculated by using the focus point. The focus point are also separated by using the rotated distance called the 2c. Ellipse are refered to as the closed curve. The ellipse curve does not pass through the point of apex.
The rotated ellipse equation are given as,
Equation for rotated ellipse is r_{1} + r_{2} = 2a.
where,
Example for rotated ellipse equation :
Given the following equation 6x^{2} + 4y^{2} = 2
a) Find the x intercepts and y intercepts of the graph for the following equation.
Solution:
Step 1: First step is to write the given equation in standard form by dividing both sides of the equation using the value 2,
6x^{2} + 4y^{2} = 2
3x^{2} + 2y^{2} = 1
Condition used in the rotated ellipse equation is a>b. So, assign a = 3 and b = 2.
Step 2: Set y = 0 in the equation obtained in the above step for finding the x intercept value.
3x^{2} = 1
Then we are solving for the x value,
x^{2} = 1/3
x = ± 1/3
Setting the value of x = 0 in the equation obtained and find the y intercepts.
2y^{2} =1
Then we are solving for the y value,
y^{2} =1/2
y = ± 1/2
This is the required solution for the x and y intercept.
Practice Problems for rotated ellipse equation:
Question 1: Given the following equation 26x^{2} +34y^{2} =26
a) Find the x intercepts and y intercepts of the graph for the following equation.
Question 2: Given the following equation 36x^{2} +22y^{2} =46
a) Find the x intercepts and y intercepts of the graph for the following equation.