Conic section is different slices of a cone which form different shapes. Some of the conic section regularly used in math are Circle, parabola, ellipse, and hyperbola. Each conic shape has its own set of formulas and properties. Real life conic sections are the use of these different conic section in day to day life. Applying the concepts and formula of the conic section to solve many real world scenarios where the conic shapes are involved. For example; concept of parabola is regularly used in different parts of physics. The path of the planets around the sun as focus is an ellipse.
Example 1: An arch of the garden has a parabolic shape. The height is 16 feet and a base width is 20 feet. Find the equation of the shape. (Assume the ground is the x- axis.)
Solution: The vertex will be (0, 16) and the width given is 20 feet which makes the x intercepts x = + 10 and x = -10.
The equation of the parabola using the vertex will be y = a (x+10) (x-10)
Substitute the vertex gives: 16 = a (0+10) (0-10) = -100a; a = -4/25;
The equation of the parabola is y = -4/25 (x2 – 100).
Example 2: Determine which conic section is the given equation
x2 + y2 – 4y -12 = 0?
Solution: Given equation is x2 + y2 – 4y -12 = 0.
The equation can be written as (x – 0)2 + (y – 2)2 – 16 = 0
Therefore (x – 0)2 + (y – 2)2 = 42.
Hence given is equation of a circle with center (0, 2) and radius 4 units.
Example 1: An arch of the garden has a parabolic shape. The height is 16 feet and a base width is 20 feet. Find the equation of the shape. (Assume the ground is the x- axis.)
Solution: The vertex will be (0, 16) and the width given is 20 feet which makes the x intercepts x = + 10 and x = -10.
The equation of the parabola using the vertex will be y = a (x+10) (x-10)
Substitute the vertex gives: 16 = a (0+10) (0-10) = -100a; a = -4/25;
The equation of the parabola is y = -4/25 (x2 – 100).
Example 2: Determine which conic section is the given equation
x2 + y2 – 4y -12 = 0?
Solution: Given equation is x2 + y2 – 4y -12 = 0.
The equation can be written as (x – 0)2 + (y – 2)2 – 16 = 0
Therefore (x – 0)2 + (y – 2)2 = 42.
Hence given is equation of a circle with center (0, 2) and radius 4 units.
