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What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
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Q1
What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
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The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.
Questions & Step-by-step Solutions
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Q
Q: What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
Solution:
The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.
Steps: 7
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Step 1: Identify the equation of the ellipse, which is x^2/25 + y^2/16 = 1.
Step 2: Recognize that this is in the standard form of an ellipse, where a^2 = 25 and b^2 = 16.
Step 3: Calculate 'a' by taking the square root of a^2: a = √25 = 5.
Step 4: Calculate 'b' by taking the square root of b^2: b = √16 = 4.
Step 5: Use the formula to find 'c', where c = √(a^2 - b^2).
Step 6: Substitute the values: c = √(25 - 16) = √9 = 3.
Step 7: The distance between the foci is given by 2c, so calculate 2c = 2 * 3 = 6.
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