The foci of the ellipse x^2/25 + y^2/16 = 1 are located at which points?
Practice Questions
Q1
The foci of the ellipse x^2/25 + y^2/16 = 1 are located at which points?
(±3, 0)
(±4, 0)
(±5, 0)
(±6, 0)
Questions & Step-by-Step Solutions
The foci of the ellipse x^2/25 + y^2/16 = 1 are located at which points?
Step 1: Identify the equation of the ellipse, which is x^2/25 + y^2/16 = 1.
Step 2: Recognize that in the standard form of an ellipse, a^2 is the denominator of x^2 and b^2 is the denominator of y^2. Here, a^2 = 25 and b^2 = 16.
Step 3: Calculate a and b by taking the square roots: a = √25 = 5 and b = √16 = 4.
Step 4: Use the formula for the distance to the foci, c = √(a^2 - b^2). Substitute the values: c = √(25 - 16).
Step 5: Simplify the expression: c = √9 = 3.
Step 6: The foci of the ellipse are located at (±c, 0). Since c = 3, the foci are at (3, 0) and (-3, 0).
