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## 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:

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.

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:

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.

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 of opposite sign.

So the conic is a hyperbola.

Question 6.

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

Solution:

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.

### 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

(i) x^{2} – 4y^{2} + 6x + 16y – 11 = 0

(ii) y^{2} – 8y + 4x – 3 = 0

(iii) 4x^{2} – 9y^{2} = 36

(iv) 16x^{2} + 25y^{2} = 400

(v) 16x^{2} + 9y^{2} + 32x – 36y – 92 = 0

(vi) x^{2} + 4y^{2} – 8x – 16y – 68 = 0

(vii) x^{2} + y^{2} – 4x + 6y – 17 = 0

Solution:

(i) Hyperbola

(ii) Parabola

(iii) Hyperbola

(iv) Ellipse

(v) Ellipse

(vi) Ellipse

(vii) Circle