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1. PRESENTATION ON HYPERBOLA Submitted by: Jerah Bagwan SUBMITTED TO: MA’AM RONELIA CABANG

2. What is hyperbola? A hyperbola is a type of conic section formed when a plane intersects a double cone at an angle such that is intersects both halves of the cone. It consists of two separate curves (branches) that are mirror images of each other. Key characteristics: two foci, two vertices, a center, And asymptotes.

3. A hyperbola is he set of all points in a plain such that the difference of the distances between two fixed points is constant. Foci : Two fixed points. Vertices : Points on the hyperbola closest to each other. Center : Midpoint between the foci and vertices.

4. Key Components Foci : Two points inside the hyperbolic curve that define its shape. Vertices: The points where the hyperbola intersects its major axis. Center: The midpoint of the line segment connecting the foci. Transverse Axis: The line segment connecting the vertices. Conjugate Axis: The line segment through the center, perpendicular to the transverse axis. Asymptotes: Lines that the hyperbola approaches as it extends to infinity.

5. Standard Equation Horizontal Hyperbola:   Center : Vertices: Foci: ±   Vertical Hyperbola:   Center: Vertices: Foci:  

6. Distance form the center to each co-vertex Distance from the center to each vertex. Distance for the center to each focus. Graphing Hyperbolas: Write the equation is standard form. Find the center Determine whether the hyperbola is horizontal or vertical. Find a and b. Find the ve rt ices Draw a rectangular using a and b from the center. Draw asymptotes through the corners of the rectangle. Sketch the hyperbola using the vertices and asymptotes. Find the foci c).  

7. Properties Hyperbolas have two axes of symmetry. The asymptotes intersects at the center of the hyperbola. The distance between the vertices is 2a. For any point on the hyperbola, the absolute difference distance to the two foci is constant and equal to 2a.

8. Hyperbolas are fascinating curves with significant application in various fields. Understanding their properties and equations allows us to analyze and appreciate their role in the world around us.