what is ellipse , hyperbola , parabola and straight line in mathematics
Answer (1)
1. Straight LineThe simplest curve.It extends infinitely in two directions with constant slope.Equation form: [tex]$\sf{y = mx + b}$[/tex], where m is the slope and b is the y-intercept.2. ParabolaA U-shaped curve.Formed when a plane cuts a cone parallel to its side.Equation form (basic): [tex]$\sf{y = ax^2 + bx + c}$[/tex].Example: the path of a ball thrown in the air.3. EllipseAn oval-shaped curve.Formed when a plane cuts through a cone at an angle, but not steep enough to reach the base.Equation form: [tex]$\sf{\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1}$[/tex] (with [tex]$\sf{a > b}$[/tex]).Example: the orbits of planets around the sun.4. HyperbolaA curve with two separate “branches” that open away from each other.Formed when a plane cuts through both halves of a cone.Equation form: [tex]$\sf{\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1}$[/tex].Example: the shape of certain satellite dish cross-sections or navigation paths.
