You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3

Identify the type of conic section for each of the equations.

Question 1.

2x^{2} – y^{2} = 7

Solution:

A = 2, B = 0, C = -1, F = -7

A ≠ C, A, and C are of opposite signs.

∴ It is a hyperbola.

Question 2.

3x^{2} + 3y^{2} – 4x + 3y + 10 = 0

Sol. Comparing this equation with the general equation of the conic

Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0

We get A = C also B = 0

So the given conic is a circle.

Question 3.

3x^{2} + 2y^{2} = 14

Solution:

Comparing this equation with the general equation of the conic

Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0

We get A ≠ C also C are of the same sign.

So the given conic is an ellipse.

Question 4.

x^{2} + y^{2} + x – y = 0

Solution:

A = 1, B = 0, C = 1, D = 1, E = -1

A = C and B = 0 (No xy term)

∴ It is a circle.

Question 5.

11x^{2} – 25y^{2} – 44x + 50y – 256 = 0

Solution:

Comparing this equation with the general equation of the conic

Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0

We get A ≠ C. Also A and C are opposite signs.

So the conic is a hyperbola.

Question 6.

y^{2} + 4x + 3y + 4 = 0

Solution:

A = 0, B = 0, C = 1, D = 4, E = 3, F = 4

B = 0 and A = 0 (either A or C = 0)

∴ It is a parabola.

### Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3 Additional Problems

Identify the type of conic section for each of the following equations

- x
^{2}– 4y^{2}+ 6x + 16y – 11 = 0 - y
^{2}– 8y + 4x – 3 = 0 - 4x
^{2}– 9y^{2}= 36 - 16x
^{2}+ 25y^{2}= 400 - 16x
^{2}+ 9y^{2}+ 32x – 36y – 92 = 0 - x
^{2}+ 4y^{2}– 8x – 16y – 68 = 0 - x
^{2}+ y^{2}– 4x + 6y – 17 = 0

Solution:

- Hyperbola
- Parabola
- Hyperbola
- Ellipse
- Ellipse
- Ellipse
- Circle