**NCERT Solutions for Class 11 Maths Chapter 10 ****Conic Sections**** Ex 10.3**

**In each of the Exercises 1 to 9, find the coordinates of the foci, the
vertices, the length of major axis, the minor axis, the eccentricity and the
length of the latus rectum of the ellipse.**

**Ex 10.3 Class 11 Maths Question 1.**

x^{2}/36 + y^{2}/16 = 1

**Solution:**

The given equation of ellipse is: x^{2}/36 + y^{2}/16 = 1

Clearly, 36 > 16

The equation of ellipse in standard form is:

**Ex 10.3 Class 11 Maths Question 2.**

x^{2}/4 + y^{2}/25 = 1

**Solution:**

The given equation of ellipse is: x^{2}/4 + y^{2}/25 = 1

Clearly, 25 > 4

The equation of ellipse in standard form is:

**Ex 10.3 Class 11 Maths Question 3.**

x^{2}/16 + y^{2}/9 = 1

**Solution:**

The given equation of ellipse is: x^{2}/16 + y^{2}/9 = 1

Clearly, 16 > 9

Here, a^{2} =
16 ⇒ a = 4 and b^{2} = 9 ⇒ b = 3.

Major axis is along x-axis.

Also, c^{2} = a^{2} – b^{2} = 16 – 9 =
7 ⇒ c = √7

Coordinates of foci (±c, 0), i.e., (±√7, 0).

Vertices are (±a, 0), i.e., (±4, 0).

Length of major axis = 2a = 2 × 4 = 8.

Length of minor axis = 2b = 2 × 3 = 6.

∴ Eccentricity e = c/a = √7/4

Also, Latus rectum = 2b^{2}/a = (2×9)/4 = 9/2.

** **

**Ex 10.3 Class 11 Maths Question 4.**

x^{2}/25 + y^{2}/100 = 1

**Solution:**

The given equation of ellipse is: x^{2}/25 + y^{2}/100 = 1

Clearly, 100 > 25

The equation of ellipse in standard form is:

** **

**Ex 10.3 Class 11 Maths Question 5.**

x^{2}/49 + y^{2}/36 = 1

**Solution:**

The given equation of ellipse is: x^{2}/49 + y^{2}/36 = 1

Clearly, 49 > 36

The equation of ellipse in standard form is:

** **

**Ex 10.3 Class 11 Maths Question 6.**

x^{2}/100 + y^{2}/400 = 1

**Solution:**

The given equation of ellipse is: x^{2}/100 + y^{2}/400 = 1

Clearly, 400 > 100

The equation of ellipse in standard form is:

**Ex 10.3 Class 11 Maths
Question 7.**

36x^{2} + 4y^{2} = 144

**Solution:**

The given equation of ellipse is: 36x^{2} + 4y^{2} =
144

**Ex 10.3 Class 11 Maths
Question 8.**

16x^{2} + y^{2} = 16

**Solution:**

The given equation of ellipse is: 16x^{2} + y^{2} =
16

**Ex 10.3 Class 11 Maths
Question 9.**

4x^{2} + 9y^{2} = 36

**Solution:**

The given equation of ellipse is: 4x^{2} + 9y^{2} =
36

**In each of the following Exercises
10 to 20, find the equation for the ellipse that satisfies the given
conditions:**

**Ex 10.3 Class 11 Maths
Question 10.**

Vertices (±5, 0), foci (±4, 0)

**Solution:**

Clearly, the foci (±4, 0) lie on the x-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 11.**

Vertices (0, ±13), foci (0, ±5)

**Solution:**

Clearly, the foci (0, ±5) lie on the y-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 12.**

Vertices (±6, 0), foci (±4, 0)

**Solution:**

Clearly, the foci (±4, 0) lie on the x-axis.

∴ The equation of ellipse in standard form is:

**Ex 10.3 Class 11 Maths
Question 13.**

Ends of major axis (±3, 0), ends of minor axis (0, ±2)

**Solution:**

Since, ends of major axis (±3, 0) lie on the x-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths Question 14.**

Ends of major axis (0, ±√5), ends of minor
axis (±1, 0)

**Solution:**

Since, ends of major axis (0, ±√5) lie on y-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 15.**

Length of major axis 26, foci (±5, 0)

**Solution:**

Since the foci (±5, 0) lie on the x-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 16.**

Length of minor axis 16, foci (0, ±6)

**Solution:**

Since the foci (0, ±6) lie on y-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 17.**

Foci (±3, 0), *a* = 4

**Solution:**

Since the foci (±3, 0) lie on the x-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 18.**

b = 3, c = 4, centre at the origin; foci on the x-axis.

**Solution:**

Since the foci lie on the x-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 19.**

Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2)
and (1, 6).

**Solution:**

Since the major axis is along the y-axis.

∴ The equation of ellipse in standard form
is:

**Ex 10.3 Class 11 Maths
Question 20.**

Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

**Solution:**

Since the major axis is along the x-axis.

∴ The equation of ellipse in standard form
is: