Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 10

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IMPORTANT

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The lines $p (p^{2} + 1) x - y + q = 0$ and ${(p^{2} + 1)}^{2} x + (p^{2} + 1) y + 2 q = 0$ are perpendicular to a common line for

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Important Questions on Point and Straight Line

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 11

The line

L

given by

\frac{x}{5} + \frac{y}{b} = 1

passes through the point

(13, 32)

, the line

K

is parallel to

L

and has the equation

\frac{x}{c} + \frac{y}{3} = 1

, then the distance between

L

and

K

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 12

The line

x + y = |a|

and

a x - y = 1

intersect each other in the first quadrant. Then, the set of all possible values of

a

in the interval

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 13

If

A (2, - 3)

and

B (- 2, 1)

are two vertices of a triangle and third vertex moves on the line

2 x + 3 y = 9,

then the locus of the centroid of the triangle is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 14

If the line

2 x + y = k

passes through the point which divides the line segment joining the points

(1, 1)

and

(2, 4)

in the ratio

3 : 2,

then

K

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 15

A line is drawn through the point

(1, 2)

to meet the coordinate axes at

P

and

Q

such that it forms a triangle

O P Q,

where

O

is the origin. If the area of the triangle

O P Q

is least, then the slope of the line

P Q

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 16

A ray of light along

x + \sqrt{3} y = \sqrt{3}

gets reflected upon reaching

X -

axis, the equation of the reflected ray is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 17

The

x

-coordinates of the incentre of the triangle that has the coordinates of midpoints of its sides as

(0, 1),

(1, 1)

and

(1, 0)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-3>Q 18

If

P S

is the median of the triangle with vertices

P (2, 2)

,

Q (6, - 1)

and

R (7, 3),

then equation of the line passing through

(1, - 1)

and parallel to

P S

is