Parabola is the graph of the quadratic equation and Pascal very well stated that parabola is known as the production of a circle. Galileo very well explained that projectiles falling into the effect of uniform gravity will be following a particular path which will be known as the concept of the parabola. Different kinds of physical motions of bodies follow different kinds of the curvilinear path which is the main reason that people need to be clear about the concept of the parabola and in the world of mathematics any kind of plane curve which will be mirror-symmetrical and will be of usually U shape alphabet will be known as the concept of the parabola.
Parabola will be referring to the equation of the curve such that the point on the curve will be equal distance from the fixed point as well as the fixed-line. The fixed point will be known as the focus of the parabola and the fix the line will be known as the directrix of the parabola. The important point to be noted over here is that it will never lie on the fixed line and the locus of any point which will be equal distance from the given point will be known as a parabola. Parabola is the most important curve of the coordinate geometry which people need to study.
It is very much important for people to be clear about the basic equation which is known as the standard equation of regular parabola as well which is known as Y Square is equal to 4 into AX.
The basic parts and features of the parabola have been explained as follows:
- Point A,0 is known as the focus
- A line drawn parallel to the Y-axis will be passing through the point -A, 0 is known as the directrix of the parabola this is perpendicular to the axis of the parabola.
- The focal chord of the parabola will be the chord that will be passing through the focus of the parabola and it will be cutting the parabola at two distinct points.
- The distance of points X1, Y1 on the parabola from the focus will be known as the focal distance and this is also equal to the perpendicular distance of the point from the direct tricks.
- The focal chord that will be perpendicular to the axis of the parabola will be passing through the focus of the parabola and this is known as the latus rectum.
- The ratio of the distance of a point from the focus to the distance of the point from the directrix will be known as eccentricity.
Being very much clear about the basic formulas associated with this particular concept is very much important and some of the basic things have been explained as follows:
- The direction of the parabola will be determined by the value of alphabet A
- Vertex H, K is the basic formula where H is equal to minus B/2A and K is equal to the function of H.
- Latus rectum is the formula denoted by four into the value of A
- Focus over here will be the concept of H, K +1/4A
- Directrix will be the formula of Y is equal to K -1/4A
Apart from all the above-mentioned points, it is also very much burden for people to be clear about the properties and derivation of the basic formulas in this particular case so that there is no chance of any kind of doubt and further, depending on platforms like Cuemath is the perfect approach of having a good hold over the topic of the parabola as well as hyperbola very easily.