Important Parabola Formulas for JEE

Since the parabola equation is y²-4x-4y = 0, Compute the vertex, focus, directrix of the parabola. If the focus of the parabola is S(x1,y1) and the equation of the guide is x+ for +c=0, then there is an equation for the parabola. If the focus coordinates are (0, 5) and the guide rail equation is y = -5, find the parabola equation.

For a parabola y² = 16x, find the coordinates of its focus, the length of the rectum, and the directrix equation.

General Equation for a Parabola:

The general equation for a parabola with vertex at (0, 0) has the form y² = 4ax and opens to the right. This is obviously a parabola with vertices and an axis parallel to the y-axis. Two parabolas with a common vertex and axis along the x and y axes intersect in the first quadrant.

Parts related to Parabola:

• A straight line passing through a fixed point A, with respect to which a right circular cone is symmetrical, is called the AXIS of the cone.
• The intersection point A of the conic with the Axis is called the TOP.
• Vertex -The vertex is the intersection point of the parabola and the axis of symmetry.
• If the area of ​​a triangle whose vertex is at the vertex of the parabola is y² + 4 (x – a²) = 0, and the other two vertices are the intersection points of the parabola and the y-axis, then it is equal to 250 square meters.
• If the x² term goes into the parabolic equation, the symmetry axis runs along the Y axis. Since the point (at2, 2at) satisfies the equation y2 = 4ax, the parametric coordinates of any point on the parabola are (at2, 2at). The tangent equation of the parabola at the point (x,y) y² = 4ax is yy = 2a (x + x) or yy – 2a (x + x) = 0, usually expressed as T = 0 from the point (x 1, y 1 ) to the parabola y² = 4ax, with T = 0, i.e. yy 1 – 2a (x + x 1) = 0.

Parabolic Chord Equation:

• The parabolic chord equation y² = 4ax for the midpoint (x1, y1) is T = S1. Let y² = 4ax or y² – 4ax = 0
• The given parabola is represented by S(x, y) = 0 S(x, y) = 0 x . If the three normals drawn from a given point (h, k) on any parabola y² = 4ax are real numbers. Let P be the intersection of the parabola y² = 12x and the common tangent of the hyperbola 8x² – y² = 8.
• If the tangent and normal of the parabola S = 0 drawn at P intersect the x-axis in T and GG respectively, then P, T, G lie on a circle centred at the focal point and having a radius equal to the focal length P 3x² ellipse + 5y² = 32 The tangent and normal at point P (2,2) intersect the x-axis at Q and R, respectively.
• Any three points of a normal parabola at which they pass through a common point are called conformal points.

Parabola:

• A parabola is the set of all points in a plane that are equidistant from a given point and a given line.
• The point is called the focus of the parabola and the line is called the directrix.
• Focus Chord- Any chord that goes through its focus is called a focus chord.

Equation: ax² + 2hxy + by² + 2gx + 2fy + c = 0

It will represent a pair of lines if abc + 2fgh – af² – ch2 – bg² = 0, otherwise any of the four conic sections.

Now that you know all this, you want to distinguish between a second order conic section equation and a pair of second order straight line equations. The general equation for a conic section is the general second power equation Ax² + 2Bxy + Cy² + 2Dx+ 2Ey + F = 0. The goal is to convert the equation 16x² + 9y² -92x -256y -24xy + 76 = 0 into the general formula for a conic sections.

You may be wondering how one equation can represent both straight pairs and conic sections. The easiest way to do this is to partially differentiate the equation of the conic with respect to x and y and simultaneously solve x and y from the two resulting equations. The parabola equation of this type has the form x² \u003d 4ay, a\u003e 0.

Also read: Inverse Trigonometric Functions in Maths

FAQs

What is maximum parabola?

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.

What moves the parabola left and right?

The parent function for a parabolic function is where is the center of the parabola. To shift the parabola left or right, the value of h changes. Since there is a negative sign in the parent function, a positive value moves the parabola to the left and a negative value moves it to the right.