RD Sharma Class 11 Solutions Chapter 27 Exercise 27.1 (Updated for 2023)

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RD Sharma Solutions Class 11 Maths Chapter 27 Exercise 27.1

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Access answers to RD Sharma Solutions Class 11 Maths Chapter 27 Exercise 27.1- Important Question with Answers

1. The equation of the directrix of a hyperbola is x – y + 3 = 0. Its focus is (-1, 1) and eccentricity 3. Find the equation of the hyperbola.

Solution:

2. Find the equation of the hyperbola whose

(i) focus is (0, 3), directrix is x + y – 1 = 0 and eccentricity = 2

(ii) focus is (1, 1), directrix is 3x + 4y + 8 = 0 and eccentricity = 2

(iii) focus is (1, 1) directrix is 2x + y = 1 and eccentricity =√3

(iv) focus is (2, -1), directrix is 2x + 3y = 1 and eccentricity = 2

(v) focus is (a, 0), directrix is 2x + 3y = 1 and eccentricity = 2

(vi)focus is (2, 2), directrix is x + y = 9 and eccentricity = 2

Solution:

Hyperbola Ex 27.1 Q2(i)

Hyperbola Ex 27.1 Q2(ii)

Hyperbola Ex 27.1 Q2(iii)

Hyperbola Ex 27.1 Q2(iv)

Hyperbola Ex 27.1 Q2(v)

Hyperbola Ex 27.1 Q2(vi)

3. Find the eccentricity, coordinates of the foci, equations of directrices, and length of the latus-rectum of the hyperbola.
(i) 9x² – 16y² = 144

(ii) 16x² – 9y² = -144

(iii) 4x² – 3y² = 36

(iv) 3x² – y² = 4

Solution:

Hyperbola Ex 27.1 Q3(i)

Hyperbola Ex 27.1 Q3(ii)

Hyperbola Ex 27.1 Q3(iii)


Hyperbola Ex 27.1 Q3(iv)

4. Find the axes, eccentricity, latus-rectum and the coordinates of the foci of the hyperbola 25x² – 36y² = 225.

Solution:

5. Find the centre, eccentricity, foci and directions of the hyperbola
(i) 16x² – 9y² + 32x + 36y – 164 = 0

(ii) x² – y² + 4x = 0

(iii) x² – 3y² – 2x = 8

Solution:

Hyperbola Ex 27.1 Q5(i)



Hyperbola Ex 27.1 Q5(ii)


Hyperbola Ex 27.1 Q5(iii)


Hyperbola Ex 27.1 Q6(i)

Hyperbola Ex 27.1 Q6(ii)


Hyperbola Ex 27.1 Q6(iii)

Hyperbola Ex 27.1 Q7(i)


Hyperbola Ex 27.1 Q7(ii)


Hyperbola Ex 27.1 Q7(iii)


Hyperbola Ex 27.1 Q7(iv)

Hyperbola Ex 27.1 Q8

Hyperbola Ex 27.1 Q9(i)


Hyperbola Ex 27.1 Q9(ii)


Hyperbola Ex 27.1 Q10

Hyperbola Ex 27.1 Q11(i)

Hyperbola Ex 27.1 Q11(ii)

Hyperbola Ex 27.1 Q11(iii)

Hyperbola Ex 27.1 Q11(iv)

Hyperbola Ex 27.1 Q11(v)

Hyperbola Ex 27.1 Q11(vi)


Hyperbola Ex 27.1 Q11(vii)


Hyperbola Ex 27.1 Q11(viii)

Hyperbola Ex 27.1 Q11(ix)


Hyperbola Ex 27.1 Q11(x)

Hyperbola Ex 27.1 Q12

Hyperbola Ex 27.1 Q13

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