Ellipse Tutor
The shape of an ellipse can be defined as the closed surface formed by the curved line in which the sum of the distances of any point on the curved line from the two points that define the ellipse is always constant. In simple words the ellipse may be defined as an oval shape. In the following article we will discuss more about the topic ellipse tutor.
Understanding Ellipse Definition is always challenging for me but thanks to all math help websites to help me out.
Understanding Ellipse Definition is always challenging for me but thanks to all math help websites to help me out.
The shape of the ellipse is a curved shape where each point on the circumference is defined by the two foci. The entire ellipses have a major axis denotes by a and also a minor axis denoted by b, where the major axis is the largest diameter of the ellipse and the minor axis is the smaller diameter of the ellipse. The Foci are the two points that define the shape of the ellipse. The general equation for any ellipse with the center at origin is given by,
`x^2/a^2+y^2/b^2 = 1`
Where, a and b are the major and the minor axis respectively. This is for the horizontal ellipse while for the vertical ellipse the major axis or a is written below y. The equation for the ellipse with the center at (h,k) is,
`(x-h)^2/a^2+(y-k)^2/b^2 = 1`
For any ellipse with the center at (h,k) and vertical major axis the foci are at `(h,k+c)` , `(h,k-c)` , While for the horizontal major axis the foci are `(h+c,k)` ,`(h-c,k)` Where c is calculated as,
`c = sqrt (a^2-b^2)`
Math is widely used in day to day activities watch out for my forthcoming posts on Area of an Ellipse and 4th grade math problems online. I am sure they will be helpful.
Example problem on ellipse tutor:
1. Find the equation of the horizontal ellipse with the center at (0,2) and a = 5 and b = 4. Also find Foci.
Solution:
The equation for the horizontal ellipse is `(x-h)^2/a^2+(y-k)^2/b^2 = 1`
`(x-0)^2/5^2+(y-2)^2/4^2 = 1`
`x^2/25+(y-2)^2/16 = 1`
For the horizontal ellipse the foci are at (h,k+c), (h,k-c)
`c = sqrt (5^2-4^2)`
`= sqrt (25-16)`
`= sqrt (9)`
`= +3 or -3`
The foci are at (3,1), (-3,1)
Practice problem on ellipse tutor:
1. Find the equation and the foci of the vertical ellipse with center (-2,1) and a= 4 and b = 3.
Answer: ` (x-1)^2/25+(y-1)^2/16 = 1` and Foci are (-2,1+√7), (-2,1-√7)
`x^2/a^2+y^2/b^2 = 1`
Where, a and b are the major and the minor axis respectively. This is for the horizontal ellipse while for the vertical ellipse the major axis or a is written below y. The equation for the ellipse with the center at (h,k) is,
`(x-h)^2/a^2+(y-k)^2/b^2 = 1`
For any ellipse with the center at (h,k) and vertical major axis the foci are at `(h,k+c)` , `(h,k-c)` , While for the horizontal major axis the foci are `(h+c,k)` ,`(h-c,k)` Where c is calculated as,
`c = sqrt (a^2-b^2)`
Math is widely used in day to day activities watch out for my forthcoming posts on Area of an Ellipse and 4th grade math problems online. I am sure they will be helpful.
Example problem on ellipse tutor:
1. Find the equation of the horizontal ellipse with the center at (0,2) and a = 5 and b = 4. Also find Foci.
Solution:
The equation for the horizontal ellipse is `(x-h)^2/a^2+(y-k)^2/b^2 = 1`
`(x-0)^2/5^2+(y-2)^2/4^2 = 1`
`x^2/25+(y-2)^2/16 = 1`
For the horizontal ellipse the foci are at (h,k+c), (h,k-c)
`c = sqrt (5^2-4^2)`
`= sqrt (25-16)`
`= sqrt (9)`
`= +3 or -3`
The foci are at (3,1), (-3,1)
Practice problem on ellipse tutor:
1. Find the equation and the foci of the vertical ellipse with center (-2,1) and a= 4 and b = 3.
Answer: ` (x-1)^2/25+(y-1)^2/16 = 1` and Foci are (-2,1+√7), (-2,1-√7)