Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 48

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Find equations of acute and obtuse angle bisectors of the angle between the lines $4 x + 3 y - 7 = 0$ and $24 x + 7 y - 31 = 0 .$ Also comment in which bisector origin lies.

Important Questions on Point and Straight Line

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 49

Find the equation of a straight line passing through the point

(4, 5)

and equally inclined to the lines

3 x = 4 y + 7

and

5 y = 12 x + 6 .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 50

The line

x + 3 y - 2 = 0

bisects the angle between a pair of straight lines of which one has equation

x - 7 y + 5 = 0,

then find equation of other line.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 51

Find the value of

λ

such that lines

x + 2 y = 3, 3 x - y = 1

and

λ x + y = 2

can not form a triangle.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 52

Find values of

λ

for which line

y = x + 1, y = λ x + 2

and

y = (λ^{2} + λ - 1) x + 3

are concurrent.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 53

Find the equation to the straight line passing through the point

(3, 2)

and the point of intersection of the lines

2 x + 3 y = 1

and

3 x - 4 y = 6

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 54

(ii)

The intersection of the lines

x + 2 y + 3 = 0

and

3 x + 4 y + 7 = 0

and perpendicular to the straight line

y - x = 8

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 55

Find the locus of the circumcentre of a triangle whose two sides are along the coordinate axes and third side passes through the point of intersection of the lines

a x + b y + c = 0

and

l x + m y + n = 0

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 56

If the slope of one of the lines represented by

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

be the

n^{th}

power of the other, then prove that

{(a b^{n})}^{\frac{1}{n + 1}} + {(a^{n} b)}^{\frac{1}{n + 1}} + 2 h = 0

.