A straight line L is perpendicular to the line 5 x - y = 1 . The area of the triangle formed by line L and the coordinate axes is 5 . Find the equation of line L .

As we know any line perpendicular to the line a x + b y + c = 0 is of type b x - a y + K = 0 . So line perpendicular to 5 x - y - 1 = 0 is - x - 5 y + K = 0 x -intercept = K ( y = 0 ) y -intercept = K 5 ( x = 0 ) Area of triangle O A B = 1 2 × O A × O B = 5 ⇒ K × K 5 = 10 ⇒ K = ± 5 2 ∴ The equation of the line is - x - 5 y + 5 2 = 0 or - x - 5 y - 5 2 = 0

MEDIUM

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IMPORTANT

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Circle are drawn which are orthogonal to both the circles $S \equiv x^{2} + y^{2} - 16 = 0$ and $S^{'} \equiv x^{2} + y^{2} - 8 x - 12 y + 16 = 0$ . If tangents are drawn from the centre of the variable circles to $S$ . Then find the locus of the mid point of the chord of contact of these tangents.

Important Questions on Point and Straight Line

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 12

Find the locus of the mid point of the chord of a circle

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

such that the segment intercepted by the chord on the curve

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

subtends a right angle at the origin.

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 13

The area of a triangle is

5

sq.units. Two of its vertices are

(2, 1)

and

(3, - 2) .

The third vertex lies on

y = x + 3 .

Find the third vertex.

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 14

A straight line

L

is perpendicular to the line

\Rightarrow 2 (\frac{16 h}{h^{2} + k^{2}}) - 3 (\frac{16 k}{h^{2} + k^{2}}) = 8

. The area of the triangle formed by line

L

and the coordinate axes is

5 .

Find the equation of line

L

MEDIUM

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 15

A line cuts the

x

-axis at

A (7, 0)

and the

y

-axis at

B (0, - 5)

. A variable line

P Q

is drawn perpendicular to

A B

cutting the

x

-axis in

P

and the

y

-axis in

Q

. If

A Q

and

B P

intersect at

R

, find the locus of

R

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 16

The vertices of a triangle

O B C

are

O (0, 0) B (- 3, - 1)

and

C (- 1, - 3) .

Find the equation of line parallel to

B C

and intersecting the sides

O B

and

O C,

whose perpendicular distance from the point

(0, 0)

\frac{1}{2}

units.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 17

The straight lines

3 x + 4 y = 5

and

4 x - 3 y = 15

intersect at the point

A

. The points

B

and

C

are chosen respectively on these lines such that

A B = A C

. Determine the equations of the line

B C

passing through the point

(1, 2)

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 18

Find the equation of the line which bisects the obtuse angle between the lines

x - 2 y + 4 = 0

and

4 x - 3 y + 2 = 0

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-4>Q 19

Show that all the chords of the curve

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

which subtend a right angle at the origin are concurrent. Also find the point of concurrency.

Circle are drawn which are orthogonal to both the circles S≡x2+y2-16=0 and S'≡x2+y2-8x-12y+16=0. If tangents are drawn from the centre of the variable circles to S. Then find the locus of the mid point of the chord of contact of these tangents.

Important Questions on Point and Straight Line

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Circle are drawn which are orthogonal to both the circles $S \equiv x^{2} + y^{2} - 16 = 0$ and $S^{'} \equiv x^{2} + y^{2} - 8 x - 12 y + 16 = 0$ . If tangents are drawn from the centre of the variable circles to $S$ . Then find the locus of the mid point of the chord of contact of these tangents.