Question

Give all formula of "Parabola "

class 11th as per JEE syllabus

Answer 1

see this attachment . you will get some help .

hope my answer will help you in some way .
Be brainly.

Answer 2

General form of equation of Parabola

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

The expression B2 - 4AC is the discriminant which is used to determine the type of conic section represented by equation.

If equation fulfills these conditions, then it is parabola.

B2 -  4AC = 0

Example

Given equation is 6x2 + 12x – y + 15 = 0, find whether it is the equation of parabola or not?

Solution: Here A = 6, B = 0, C = 0

Determinant will be B2 - 4AC

= 0-4(6) (0) = 0

This shows that B2 - 4AC = 0 so this is parabola or in other way we can say that only one variables is squared, so this is parabola.


Standard form of equation of Parabola

Cartesian coordinates are the points on a plane with a pair of numerical coordinates which represented by (x, y)

 If the vertex is at the origin and the axis of symmetry lies on x-axis

There will be two situations possible if the vertex is at the origin and the axis of symmetry lies on the x-axis, the parabola is either on the positive side of x- axis or on the negative side of the x-axis.

If p >0 and  pw lies on the positive x-axis

y2 = 4px

Here, p is the distance from vertex to focus on the x axis. So the coordinates of F = (p, 0), which shows that it lies on the positive side of x-axis. Directrix is at x = -p, as it is equidistant from the vertex as vertex is from focus. This shows that if p > 0, then the parabola opens towards right.


If p < 0 and p lies on negative x-axis

y2 = -4px

Here, p is the distance from vertex to focus on the x axis, which is negative. So the coordinates of F = (-p, 0), which shows that it lies on the x-axis, but on the negative side.

Directrix is at x = p, as it is equidistant from the vertex as vertex is from focus .this shows that if p < 0, then the parabola opens towards left.



 If the vertex is at the origin and the axis of symmetry lies on y-axis

There will be two situations possible if the vertex is at the origin and the axis of symmetry lies on the y-axis that the parabola is either on the positive side of y- axis or on the negative side of the y-axis.

If p >0 and p lies on the positive y-axis

x2 = 4py

Here, p is the distance from vertex to focus on the y-axis. So the coordinates of F = (0, p), which shows that it lies on the y-axis.

Directrix is at y = -p, as it is equidistant from the vertex as vertex is from focus .this shows that if p > 0, then the parabola opens upwards.



If p < 0 and p lies on negative y-axis

​x2 = -4py

Here, p is the distance from vertex to focus on the y axis, which is negative. So the coordinates of F = (0,-p)), which shows that it lies on the y-axis, but on the negative side.

Directrix is at x = p, as it is equidistant from the vertex as vertex is from focus .this shows that if p < 0, then the parabola opens downwards.



Vertex form of equation of Parabola

If the vertex is not at the origin

x = p(y - k)2+ h

where p is the horizontal stretch factor, (h, k) is the coordinates of the vertex. This shows that if p > 0 that is, p is positive then the parabola opens towards right and if p < 0 that is, p is negative then the parabola opens towards left.



y = p(x - h)2 + k

where p is the vertical stretch factor. (h, k) is the coordinates of the vertex. This shows that if p > 0 that is, p is positive then the parabola goes upwards and if p < 0 that is, p is negative then the parabola goes downwards.




How do you find the focus of a Parabola?

If we have an equation of a parabola in vertex form like y = a (x−h)2 + k, it means that the vertex is at (h, k) and the focus is (h, k+1/4a)

As we know that this equation is for vertical parabola, so the x-coordinate of the focus will