# RS Aggarwal Class 11 Chapter 22 Solutions (Parabola)

RS Aggarwal Class 11 Solutions for Chapter 22 simplifies the Chapter by giving expert Solutions to the questions. Moreover, it helps students to understand the basic concepts of Parabola and terms related to it. To provide easy and free learning to students Instasolv provides RS Aggarwal Class 11 Solutions to students which is accessible by them anywhere, anytime.

The Chapter consists of 1 exercise with 18 questions in it. The Solutions to this exercise are designed by experts and are more of the examination based because the experts are highly experienced in the field. The topic becomes easy as it contains examples that make it easy for students to understand. This chapter of RS Aggarwal Solutions is important as it makes a base for Class 12 and RS Aggarwal with its simplified concepts and stepwise Solutions helps students to grasp the concepts and gain good marks in their exams.

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**Important points of the Chapter**

- A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.
- Fixed-line is called directrix of a parabola
- The point of intersection of the parabola with the axis is called the vertex.
- Equation of a parabola is simplest if the vertex is at origin and the directrix is along the x-axis or y-axis.
- Four possible options for the directrix, given vertex, are at origin: (x=a ,x= -a ,y= a, y= -a).
- The tangent at any point on a parabola bisects the angle between the focal distance of the point and the perpendicular on the directrix from the point.
- The tangent at the extremities of a focal chord of a parabola intersects at right angles on the directrix.
- The portion of the tangent to a parabola cut off between the directrix and the curve subtends a right angle at the focus.
- The perpendicular drawn from the focus on any tangent to a parabola intersects it at the point where it cuts the tangent at the vertex.
- The perpendicular distance from a focus on directrix is half the length of the latus rectum
- Vertex is the middle point of the focus and the point of intersection of directrix and axis
- Two parabolas are said to be equal if they have the same latus rectum
- The orthocentre of any triangle formed by three tangents to a parabola lies on the directrix.
- For the ends of the latus rectum of the parabola y
^{2}= 4ax, the values of the perimeter are ± 1. - The circles described on focal radii of a parabola as diameter touches the tangent at the vertex.

## Topics covered under RS Aggarwal Chapter 22 – Parabola

The different topics covered in RS Aggarwal Class 11 Chapter 22 – Parabola are:

- Standard equation of a parabola
- Latus rectum
- Focal chord properties
- Parametric co-ordinates
- Tangent to a parabola
- General equations of parabola
- Normal to a parabola
- Focal cord, tangent, and normal properties

**Important points to remember**

- The general form of a parabola: y
^{2}= 4ax

** Focus : **F(a,0)

** Vertex : **A(0,0) (at any point A)

** Equation of the directrix :** x + a = 0

** Axis: y = **0

** Length of latus rectum : **4a

- The general form of a parabola: y
^{2}= -4ax

** Focus :** F(-a,0)

** Vertex :** A(0,0) (at any point A)

** Equation of the directrix :** x – a = 0

** Axis: y =** 0

** Length of latus rectum :** 4a

- The general form of a parabola: x
^{2}= 4ay

** Focus :** F(0,a)

** Vertex : **A(0,0) (at any point A)

** Equation of the directrix :** y + a = 0

** Axis:** x = 0

** Length of latus rectum : **4a

**The general form of a parabola: x**^{2}= -4ay

** Focus : **F(0, -a)

** Vertex :** A(0,0) (at any point A)

** Equation of the directrix:** y – a = 0

** Axis: **x = 0

** Length of latus rectum: **4a

## Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 22 Parabola

This exercise has 18 questions in which you have to:

- Find the various coordinates of the equation given
- Find the length of the lactus rectum of the parabola by the given equation
- Find the equation of the parabola by the given vertex
- Find the equation of the parabola by the given focus and directrix
- Find the equation of the parabola on the axis by the given points

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