What is the equation of an ellipse with foci at (±c, 0) and vertices at (±a, 0)?
Practice Questions
Q1
What is the equation of an ellipse with foci at (±c, 0) and vertices at (±a, 0)?
x^2/a^2 + y^2/b^2 = 1
y^2/a^2 + x^2/b^2 = 1
x^2/b^2 + y^2/a^2 = 1
y^2/b^2 + x^2/a^2 = 1
Questions & Step-by-Step Solutions
What is the equation of an ellipse with foci at (±c, 0) and vertices at (±a, 0)?
Step 1: Understand that an ellipse is a shape that looks like a stretched circle.
Step 2: Identify the foci of the ellipse, which are points located at (±c, 0). This means the foci are on the horizontal axis.
Step 3: Identify the vertices of the ellipse, which are points located at (±a, 0). This means the vertices are also on the horizontal axis.
Step 4: Recognize that the major axis of the ellipse is horizontal because the foci and vertices are along the x-axis.
Step 5: Recall the standard form of the equation for an ellipse with a horizontal major axis, which is x²/a² + y²/b² = 1.
Step 6: In this equation, 'a' represents the distance from the center to the vertices, and 'b' represents the distance from the center to the endpoints of the minor axis.
Step 7: To find 'b', use the relationship c² = a² - b², where 'c' is the distance from the center to the foci.
Step 8: Substitute the values of 'a' and 'b' into the standard form equation to get the specific equation of the ellipse.
