# NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

## NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections

NCERT Solutions for Class 11 Maths Chapter 10: Conic Sections, available in both English and Hindi Medium, updated for the CBSE term exams 2024-25. Access the revised solutions for Chapter 10 of Class 11 Mathematics, based on the rationalized textbooks and the updated syllabus for the academic year 2024-25.

### 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} = 2^{2}

x^{2} +y^{2} + 4 – 4y = 4

x^{2} + y^{2} - 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}

x^{2} + 4x + 4 + y^{2} - 6y + 9 = 16

x^{2} + y^{2} + 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 y^{2} = 12x

**Ans:**

The given equation is y^{2} = 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 x^{2}= 6y

**Ans:**

The given equation is x^{2} = 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 y^{2} = 8x

**Ans:**

The given equation is y^{2} = - 8x.

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

On comparing this equation with y^{2} = -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 x^{2} = 16y

**Ans:**

The given equation is x^{2} = - 16y.

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

On comparing this equation with x_{2} = -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