NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.2 Conic Sections 2026-27

Question 1. Find the coordinates of the focus, axis of the parabola, equation of the directrix and length of the latus rectum.

Given: y² = 12x

Solution: Compare the given equation with the standard form:

y² = 4ax

So,

4a = 12

a = 3

Now,

Focus = (a, 0) = (3, 0)

Axis = x-axis (y = 0)

Directrix = x = –a = x = –3

Length of latus rectum = 4a = 12

Answer:

Focus: (3, 0)

Axis: x-axis

Directrix: x = –3

Length of latus rectum: 12 units

Question 2. Given: x² = 6y

Solution:

Compare with:

x² = 4ay

4a = 6

a = 3/2

Therefore,

Focus = (0, 3/2)

Axis = y-axis

Directrix = y = –3/2

Length of latus rectum = 6

Answer:

Focus: (0, 3/2)

Axis: y-axis

Directrix: y = –3/2

Length of latus rectum: 6 units

Question 3. Given: y² = –8x

Solution:

Compare with:

y² = –4ax

4a = 8

a = 2

Hence,

Focus = (–2, 0)

Axis = x-axis

Directrix = x = 2

Length of latus rectum = 8

Answer:

Focus: (–2, 0)

Axis: x-axis

Directrix: x = 2

Length of latus rectum: 8 units

Question 4. Given: x² = –16y

Solution:

Compare with:

x² = –4ay

4a = 16

a = 4

Therefore,

Focus = (0, –4)

Axis = y-axis

Directrix = y = 4

Length of latus rectum = 16

Answer:

Focus: (0, –4)

Axis: y-axis

Directrix: y = 4

Length of latus rectum: 16 units

Question 5. Given: y² = 10x

Solution:

Compare with:

y² = 4ax

4a = 10

a = 5/2

Thus,

Focus = (5/2, 0)

Axis = x-axis

Directrix = x = –5/2

Length of latus rectum = 10

Answer:

Focus: (5/2, 0)

Axis: x-axis

Directrix: x = –5/2

Length of latus rectum: 10 units

Question 6. Given: x² = –9y

Solution:

Compare with:

x² = –4ay

4a = 9

a = 9/4

Hence,

Focus = (0, –9/4)

Axis = y-axis

Directrix = y = 9/4

Length of latus rectum = 9

Answer:

Focus: (0, –9/4)

Axis: y-axis

Directrix: y = 9/4

Length of latus rectum: 9 units

Question 7. Find the equation of the parabola whose focus is (6, 0) and directrix is x = –6.

Solution:

For a parabola opening rightward,

Focus = (a, 0)

Directrix = x = –a

Comparing,

a = 6

Using the standard equation:

y² = 4ax

y² = 4 × 6 × x

y² = 24x

Answer: y² = 24x

Question 8. Find the equation of the parabola whose focus is (0, –3) and directrix is y = 3.

Solution:

The parabola opens downward.

Compare with:

Focus = (0, –a)

Directrix = y = a

Therefore,

a = 3

Standard equation:

x² = –4ay

x² = –12y

Answer: x² = –12y

Question 9. Find the equation of the parabola whose vertex is (0, 0) and focus is (3, 0).

Solution:

Focus = (a, 0)

Therefore,

a = 3

Equation:

y² = 4ax

y² = 12x

Answer: y² = 12x

Question 10. Find the equation of the parabola whose vertex is (0, 0) and focus is (–2, 0).

Solution:

Focus = (–a, 0)

a = 2

Equation:

y² = –4ax

y² = –8x

Answer: y² = –8x

Question 11. Find the equation of the parabola whose vertex is (0, 0), passing through (2, 3) and axis is x-axis.

Solution:

Since the axis is the x-axis, the equation is

y² = 4ax

Substitute point (2, 3):

3² = 4a × 2

9 = 8a

a = 9/8

Equation:

y² = 4 × (9/8)x

y² = (9/2)x

Multiplying by 2:

2y² = 9x

Answer: 2y² = 9x

Question 12. Find the equation of the parabola whose vertex is (0, 0), passes through (5, 2) and is symmetric about y-axis.

Solution: 

A parabola symmetric about the y-axis has the equation:

x² = 4ay

Substitute point (5, 2):

25 = 4a × 2

25 = 8a

a = 25/8

Equation:

x² = 4 × (25/8)y

x² = (25/2)y

Multiplying by 2:

2x² = 25y

Answer: 2x² = 25y

Key Takeaways from NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Conic Sections

Understanding the concepts covered in NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Conic Sections helps students build a strong foundation in coordinate geometry. This exercise primarily focuses on the parabola, including its standard equations, focus, directrix, axis, and latus rectum, which are essential for mastering conic sections.

Make sure to thoroughly study the different forms of parabola equations and their geometric properties. Regular practice of NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.2 enhances analytical thinking, improves problem-solving abilities, and strengthens preparation for the 2026–27 academic session as well as competitive exams.

Practice solving each question systematically and understand the logic behind every step. Developing conceptual clarity instead of relying solely on formulas will improve accuracy, boost confidence, and help you score better in examinations.

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Chapter-Specific NCERT Solutions for Class 11 Maths

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