Which of the following represents a hyperbola with transverse axis along the x-a
Practice Questions
Q1
Which of the following represents a hyperbola with transverse axis along the x-axis?
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
Which of the following represents a hyperbola with transverse axis along the x-axis?
Step 1: Understand what a hyperbola is. A hyperbola is a type of curve formed by the intersection of a double cone with a plane.
Step 2: Know the standard form of a hyperbola's equation. The standard form for a hyperbola with a transverse axis along the x-axis is x^2/a^2 - y^2/b^2 = 1.
Step 3: Identify the transverse axis. The transverse axis is the line segment that connects the two vertices of the hyperbola. For this type of hyperbola, it runs horizontally along the x-axis.
Step 4: Recognize the components of the equation. In the equation x^2/a^2 - y^2/b^2 = 1, 'a' represents the distance from the center to the vertices along the x-axis, and 'b' is related to the distance along the y-axis.
Step 5: Conclude that the equation x^2/a^2 - y^2/b^2 = 1 indeed represents a hyperbola with its transverse axis along the x-axis.
