Standard form of Ellipse:
Ellipse is the two dimensional closed geometric figure formed by the intersection of the circular cone and the plane cutting through the circular cone completely. The distance between any point on the ellipse and the foci is always constant one. The addition of distance between any two fixed points is constant
standard formula
The standard form of the ellipse is
` (x^2/m^2)` +`(y^2/n^2)` = 1 where m and n are greater than 0
Here
Origin is (0, 0)
The length of the major axis is 2m
The length of the minor axis is 2n
1.The equation of the ellipse is
4x2+9y2=36
a.Find the x intercept and y intercept.
b.Find the points of the foci
c.Find the length of the major and minor axis
d.Draw the graph
Solution:
Here the standard equation is
The standard form of the ellipse is
` (x^2/m^2)` +`(y^2/n^2)` = 1 where m and n are greater than 0
Here
Origin is (0, 0)
The length of the major axis is 2m
The length of the minor axis is 2n
Rewrite the equation in the standard form so, divide the entire equation by 36
` ((4x^2)/36)` + `((9y^2)/36)` = `(36/36)`
`(x^2/9)` +`(y^2/4)` = 1
Here m2= 9, m=3
n2 =4,n=2 m>n>0
a.Find the x intercept and y intercept:
To find the x intercept put y=0 in the given equation
` (x^2/9)` +0=1
x2=1*9
x2= 9
x= + or – 3
To find the y intercept put x=0 in the given equation
0 +`(y^2/4)` =1
y2=1*4
y2=4
y= + or – 2
b.Find the point of foci:
We need to find the p
p2= 9-4
p2=5
p = + or – 2.23
The foci points are (2.23, 0) and (-2.23, 0)
c.The length of the major axis and minor axis
The length of the major axis is 2m = 2*3= 6
The length of the minor axis is 2n = 2*2=4
d.We need to draw the graph
Ellipse is the two dimensional closed geometric figure formed by the intersection of the circular cone and the plane cutting through the circular cone completely. The distance between any point on the ellipse and the foci is always constant one. The addition of distance between any two fixed points is constant
standard formula
The standard form of the ellipse is
` (x^2/m^2)` +`(y^2/n^2)` = 1 where m and n are greater than 0
Here
Origin is (0, 0)
The length of the major axis is 2m
The length of the minor axis is 2n
Model problems for standard form of ellipse
1.The equation of the ellipse is
4x2+9y2=36
a.Find the x intercept and y intercept.
b.Find the points of the foci
c.Find the length of the major and minor axis
d.Draw the graph
Solution:
Here the standard equation is
The standard form of the ellipse is
` (x^2/m^2)` +`(y^2/n^2)` = 1 where m and n are greater than 0
Here
Origin is (0, 0)
The length of the major axis is 2m
The length of the minor axis is 2n
Rewrite the equation in the standard form so, divide the entire equation by 36
` ((4x^2)/36)` + `((9y^2)/36)` = `(36/36)`
`(x^2/9)` +`(y^2/4)` = 1
Here m2= 9, m=3
n2 =4,n=2 m>n>0
a.Find the x intercept and y intercept:
To find the x intercept put y=0 in the given equation
` (x^2/9)` +0=1
x2=1*9
x2= 9
x= + or – 3
To find the y intercept put x=0 in the given equation
0 +`(y^2/4)` =1
y2=1*4
y2=4
y= + or – 2
b.Find the point of foci:
We need to find the p
p2= 9-4
p2=5
p = + or – 2.23
The foci points are (2.23, 0) and (-2.23, 0)
c.The length of the major axis and minor axis
The length of the major axis is 2m = 2*3= 6
The length of the minor axis is 2n = 2*2=4
d.We need to draw the graph