Solved Examples on Ellipse
Example 1: If the length of the semi-major axis is given as 10 cm and the semi-minor axis is 7 cm of an ellipse. Find its area.
Solution:
Given, the length of the semi-major axis of an ellipse, a = 10 cm
Length of the semi-minor axis of an ellipse, b = 7 cm
We know the area of an ellipse using the formula;
Area = π x a x b
= π x 10 x 7
= 70 x π
Therefore Area = 219.91 cm2
Example 2: For an ellipse, the length of the semi-major axis is 8 cm and the semi-minor axis is 3 cm then find its area.
Solution:
Given:
Length of semi-major axis of the ellipse (a) = 8 cm
Length of semi-major axis of the ellipse (b) = 3 cm
Formula for the area of the ellipse:
Area = π x a x b
Area = π x 8 x 3
Area = 24 π cm2
Example 3: Find the lengths for the major axis and minor axis of equation 7x2+3y2= 21
Solution:
Given equation is 7x2+3y2= 21
Dividing both sides by 21, we get
x2/3 + y2/7 = 1
We know that, Standard Equation of Ellipse
x2/b2+y2/a2 = 1
As the foci lies on y-axis, for the above equation , the ellipse is centered at origin and major axis on y-axis then;
b2 = 3
b = 1.73a2 = 7
a = 2.64Thus,
Length of Major Axis = 2a
= 5.28Length of Minor Axis = 2b
= 3.46
Ellipse
An ellipse is the locus of all points on a plane with constant distances from two fixed points in the plane. The fixed points encircled by the curve are known as foci (singular focus). The constant ratio is the eccentricity of the ellipse and the fixed line is the directrix. In this article, we will learn about the ellipse in detail.
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