The length of latus rectum of an ellipse x²+ 4y²= 8
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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
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
1 answer