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What is the length of the latus rectum of the ellipse x^2/36 + y^2/16 = 1?
What is the length of the latus rectum of the ellipse x^2/36 + y^2/16 = 1?
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Q1
What is the length of the latus rectum of the ellipse x^2/36 + y^2/16 = 1?
8/3
12
16/3
24
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The length of the latus rectum is given by (2b^2/a). Here, b^2 = 16, a^2 = 36, so length = (2*16/6) = 12.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of the latus rectum of the ellipse x^2/36 + y^2/16 = 1?
Solution:
The length of the latus rectum is given by (2b^2/a). Here, b^2 = 16, a^2 = 36, so length = (2*16/6) = 12.
Steps: 8
Show Steps
Step 1: Identify the equation of the ellipse, which is given as x^2/36 + y^2/16 = 1.
Step 2: Recognize that in the standard form of an ellipse, a^2 is the denominator of the x^2 term and b^2 is the denominator of the y^2 term.
Step 3: From the equation, we see that a^2 = 36 and b^2 = 16.
Step 4: Calculate the values of a and b by taking the square roots: a = sqrt(36) = 6 and b = sqrt(16) = 4.
Step 5: Use the formula for the length of the latus rectum, which is (2b^2/a).
Step 6: Substitute the values of b^2 and a into the formula: b^2 = 16 and a = 6.
Step 7: Calculate the length of the latus rectum: (2 * 16) / 6 = 32 / 6 = 12/3 = 4.
Step 8: Therefore, the length of the latus rectum is 12.
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