What is the equation of the ellipse with center at the origin, semi-major axis 5, and semi-minor axis 3?
Practice Questions
1 question
Q1
What is the equation of the ellipse with center at the origin, semi-major axis 5, and semi-minor axis 3?
x^2/25 + y^2/9 = 1
x^2/9 + y^2/25 = 1
x^2/15 + y^2/5 = 1
x^2/5 + y^2/15 = 1
The equation of the ellipse is x^2/25 + y^2/9 = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the equation of the ellipse with center at the origin, semi-major axis 5, and semi-minor axis 3?
Solution: The equation of the ellipse is x^2/25 + y^2/9 = 1.
Steps: 7
Step 1: Identify the center of the ellipse. The center is at the origin (0, 0).
Step 2: Identify the lengths of the semi-major and semi-minor axes. The semi-major axis is 5 and the semi-minor axis is 3.
Step 3: Write the standard form of the equation of an ellipse centered at the origin: (x^2/a^2) + (y^2/b^2) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis.
Step 4: Substitute the values of 'a' and 'b' into the equation. Here, a = 5 and b = 3.
Step 5: Calculate a^2 and b^2. a^2 = 5^2 = 25 and b^2 = 3^2 = 9.
Step 6: Substitute a^2 and b^2 into the equation: (x^2/25) + (y^2/9) = 1.
Step 7: Write the final equation of the ellipse: x^2/25 + y^2/9 = 1.
