Question -
Answer -
Given:
Minor axis is equal to the distance between foci and whoselatus – rectum is 10.
Now let us find the equation to the ellipse.
We know that the equation of the ellipse whose axes are xand y – axis is given as
We know that length of the minor axis is 2b and distancebetween the foci is 2ae.
By using the formula,
Eccentricity:
We know that the length of the latus rectum is 2b2/a
It is given that length of the latus rectum = 10
So by equating, we get
2b2/a = 10
a2/ a = 10 [Since, a2 = 2b2]
a = 10
a2 = 100
Now, by substituting the value of a2 we get
2b2/a = 10
2b2/10 = 10
2b2 = 10(10)
b2 = 100/2
= 50
So the equation of the ellipse can be given as
x2 + 2y2 = 100
∴ The equation of the ellipse is x2 + 2y2 =100.