Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3 Textbook Questions and Answers, Notes.

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

Question 1.

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

(1) 2x² – y² = 7

(2) 3x² + 3y² – 4x + 3y + 10 = 0

(3) 3x² + 2y² = 14

(4) x² + y² + x – y = 0

(5) 11x² – 25y² – 44x + 50y – 256 = 0

(6) y² + 4x + 3y + 4 = 0

Solution:

(1) 2x² – y² = 7

Comparing this equation with the general equation of the conic

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

We get A = 2, C = – 1

Elere A ≠ C also A and C are of opposite signs.

So the conic is a hyperbola.

(2) 3x² + 3y² – 4x + 3y + 10 = 0

A = 3, B = 0, C = 3, D = -4, E = 3, F = 10

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

∴ It is a circle.

(3) 3x² + 2y² = 14

A = 3, B = 0, C = 2, F = -14

A ≠ C and A & C are the same signs.

∴ It is an ellipse.

(4) x² + y² + x – y = 0

Comparing this equation with the general equation of the conic

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

We get A = C and B = 0

So the given conic is a circle.

(5) 11x² – 25y² – 44x + 50y – 256 = 0

A =11, B = 0, C = -25, D = -44, E = 50, F = -256

A ≠ C and A & C are the opposite signs.

∴ It is a hyperbola.

(6) y² + 4x + 3y + 4 = 0

Comparing this equation with the general equation of the conic

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

We get A = 0 and B = 0

So the conic is a parabola.