The length of latus rectum of an ellipse x²+ 4y²= 8
What is the length of latus rectum of an ellipse x² + 4y² =8
Find equation of parabola x² + 4x+y=0
By definition:
For x^2/a^2 + y^2/b^2 = 1, the length of the latus rectum is 2b^2/a
for x^2 + 4y^2 = 8
x^2/8 + y^2/2 = 1
so a^2 = 8, and b^2 = 2, thus a = √8 = 2√2
length of LR = 2(2)/(2√2) = 2/√2 = √2
To find the length of the latus rectum of an ellipse, we need to determine the length of the chord that passes through the focus and is perpendicular to the major axis.
Step 1: First, we need to identify the equation of the given ellipse. The equation of an ellipse in standard form is (x²/a²) + (y²/b²) = 1, where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
Comparing the given equation, x² + 4y² = 8, with the standard form, we can see that a² = 8 and b² = 2.
Step 2: To determine the length of the latus rectum, we need to find the value of 'b²/a'. In our case, it is 2/8 = 1/4.
Step 3: The formula to calculate the length of the latus rectum of an ellipse is 2b²/a.
Substituting the values, we get (2 * 1/4) / √8.
Simplifying, we get 1/2 * √8.
The length of the latus rectum of the ellipse x² + 4y² = 8 is (1/2) * √8.
Please note that if the equation of the ellipse is in a different form, you may need to manipulate the equation to bring it into standard form and then follow the steps mentioned above.