Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(b)>Q III

HARD

11th Andhra Pradesh Board

IMPORTANT

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Find the product of the lengths of the perpendiculars drawn from $(2, 1)$ upon the lines $12 x^{2} + 25 x y + 12 y^{2} + 10 x + 11 y + 2 = 0$ .

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Important Questions on Pair of Straight Lines

HARD

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(b)>Q III

Show that the straight lines

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

and

x^{2} + 4 x y + 4 y^{2} + 5 x + 10 y + 4 = 0

form a parallelogram and find the lengths of its sides.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(b)>Q III

Show that the product of the perpendicular distances from the origin to the pair of straight lines represented by

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

is

\frac{| c |}{\sqrt{(a - b)^{2} + 4 h^{2}}}

.

HARD

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(b)>Q III

If the equation

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

represents a pair of intersecting lines, then show that the square of the distance of their point of intersection from the origin is

\frac{c (a + b) - f^{2} - g^{2}}{a b - h^{2}}

. Also show that the square of this distance is

\frac{f^{2} + g^{2}}{h^{2} + b^{2}}

if the given lines are perpendicular.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(c)>Q I

Find the combined equation of the lines joining the origin to the points of intersection of

x^{2} + y^{2} = 1

and

x + y - 1

.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(c)>Q I

Find the angle between the lines joining the origin to the points of intersection of

y^{2} = x

and

x + y = 1

.

HARD

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(c)>Q II

Show that the lines joining the origin to the points of intersection of the curve

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

and the straight line

x - y - \sqrt{2} = 0

are mutually perpendicular.

HARD

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(c)>Q II

Find the values of

k

, if the lines joining the origin to the points of intersection of the curve

2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0

and the line

x + 2 y = k

are mutually perpendicular.

HARD

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 4 - Pair of Straight Lines>Exercise 4(c)>Q II

Find the angle between the lines joining the origin to the points of intersection of the curve

x^{2} + 2 x y + y^{2} + 2 x + 2 y - 5 = 0

and the line

3 x - y + 1 = 0

.