NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

Conic Sections Class 11 Maths NCERT Solutions are extremely helpful while doing homework. NCERT Solutions for Class 11 Maths Chapter 11 Conic sections All Exercises were prepared by Experienced Learn CBSE.in Teachers.

Ex 11.4 and Miscellaneous Exercise PDF in hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermedite and UP Board students, who arre using NCERT books based on updated CBSE Syllabus for the session 2019-20

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1

Ex 11.1 Class 11 NaQuestion 1

Find the equation of the circle with centre (0, 2) and radius 2

Ans:

The equation of the circle with center (h, k) and radius r is given as

(x – h)² + (y - k) ² = r ²

It is given that centre (h, k) = (0, 2) and radius (r) =2.

Therefore, the equation of the circle is

(x - 0) ² + (y - 2) ² = 2²

x² +y² + 4 – 4y = 4

x² + y² - 4y = 0

Ex 11.1 Class 11 NaQuestion 2

Find the equation of the circle with centre (-2, 3) and radius 4

Ans:

The equation of the circle with center (h, k) and radius r is given as

(x – h)² + (y - k) ² = r ²

It is given that centre (h, k) = ( -2, 3) and radius (r) =4.

Therefore, the equation of the circle is

(x +2) ² + (y - 3) ² =(4) ²

x² + 4x + 4 + y² - 6y + 9 = 16

x² + y² + 4x – 6y – 3 = 0

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.2

Ex 11.2 Class 11 NaQuestion 1

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 12x

Ans:

The given equation is y² = 12x

Here, the comparing of x is positive. Hence, the parabola opens towards the right.

On comparing this eqution with y ₂ = 4ax, we obtain

Coordinates of the focus – (a, 0) = (3, 0)

Since the given equation involves y ² , the axis of the parabola is the x – axis.

Equation of direcctrix, x = a I,e, x = - 3 I , e, x + 3 = 0

Length of latus rectum = 4a = 4 x 3 = 12

Ex 11.2 Class 11 NaQuestion 2

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 6y Ans:

The given equation is x² = 6y.

Here, the comparing of y is positive. Hence, the parabola opens upwards.

On comparing this eqution with x ₂ = 4ax, we obtain

Ex 11.2 Class 11 NaQuestion 3

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 8x

Ans:

The given equation is y² = - 8x.

Here, the coefficient of x is negative. Hence, the parabola opens towards the left.

On comparing this equation with y² = -4ax, we obtain

Ex 11.2 Class 11 NaQuestion 4

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 16y

Ans:

The given equation is x² = - 16y.

Here, the coefficient of x is negative. Hence, the parabola opens downwards.

On comparing this equation with x₂ = -4ay, we obtain

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.3

Ex 11.3 Class 11 NaQuestion 1

Ex 11.3 Class 11 NaQuestion 2

Ex 11.3 Class 11 NaQuestion 3

NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.4

Ex 11.4 Class 11 NaQuestion 1

Ex 11.4 Class 11 NaQuestion 2

Class 11 Maths NCERT Solutions – Miscellaneous Questions

Miscellaneous Exercise class 11 Maths Question 1:

If a parabolic reflector is 20 cm diameter and 5 cm deep, find the focus.

Ans:

The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that axis of the reflector is along the positive x – axis.

This can be diagrammatically represented as

Miscellaneous Exercise class 11 Maths Question 1:

An arch in the form of parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

Ans:

The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the positive y- axis

This can be diagrammatically represented as