What is formula of parabola?
The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.
How do you find the Directrix of a parabola?
How to find the directrix, focus and vertex of a parabola y = ½ x2. The axis of the parabola is y-axis. Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix.
What is Directrix parabola?
A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.
How do you solve parabolas?
The solution for any quadratic equation or parabola can be found by using a little algebra and the general formula for the quadratic equation, which is : x = -b ± sqrt(b^2 – 4ac) / 2a. Figure out the coefficients a, b, and c by looking at the given formula.
How do you find the equation of a parabola?
In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that the coordinates for the focus of the parabola is (h, k+1/4a).
How do you find the Directrix and focus of an equation?
Focus & directrix of a parabola from the equation So the focus is (h, k + C), the vertex is (h, k) and the directrix is y = k – C.
What are parabolas in math?
parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. The vertex of the parabola is the point on the curve that is closest to the directrix; it is equidistant from the directrix and the focus.
Which is the formula for a parabola that opens up?
Parabola Opens Up. Standard equation of a parabola that opens up and symmetric about y-axis with vertex at origin. x 2 = 4ay. Standard equation of a parabola that opens up and symmetric about y-axis with at vertex (h, k). (x – h) 2 = 4a(y – k) Graph of x 2 = 4ay :
Which is the most important parabola equation in JEE?
Parabola is an important topic for JEE Main and JEE Advanced. The parabola formulas given here will help students not only to strengthen their foundation in the topic but also to solve different types of problems easily. 1. Equation of standard parabola: The equation of the parabola with focus at (a,0) a>0 and directrix x = -a is y2 = 4ax.
What is the equation for the latus rectum of a parabola?
The latus rectum of a parabola is the chord that passes through the focus and is perpendicular to the axis of the parabola. 2 ( 4 a. a) Note: – Two parabola are said to be equal if their latus rectum are equal. For a parabola, the equation is y 2 = -4ax.
What are the properties of a parabola curve?
A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix. Parabola is an integral part of conic section topic and all its concepts parabola are covered here.