EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2020 (9-Sep Shift-1)>Q 7

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Let $A = (0, 4)$ and $B = (2 \cos θ, 2 \sin θ),$ for some $0 < θ < \frac{π}{2} .$ Let $P$ divide the line segment $A B$ in the ratio $2 : 3$ internally. The locus of $P$ is

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Important Questions on The Straight Line

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2021 (04-Aug Shift-2)>Q 11

The locus of a point

P

which moves such that the sum of its distances from two perpendicular lines is equal to

1

is a

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2020 (9-Sep Shift-1)>Q 14

If

x \cos θ + y \sin θ = p

is the normal form and

y = m x + c

is the slope - intercept form of the line

x + 2 y + 1 = 0,

then

\tan^{- 1} (\tan θ + m + c) =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2018 (04-May Shift-1)>Q 15

The equation of the straight line in the normal form which is parallel to the lines

x + 2 y + 3 = 0

and

x + 2 y + 8 = 0

and dividing the distance between these two lines in the ratio

1 : 2

internally is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2019 (03-May Shift-2)>Q 16

If

x \cos α + y \sin α = p

is the normal form of the equation of a straight line

x + \sqrt{3} y + 4 = 0

and

a, b

are respectively

X, Y -

intercepts of this line, then

\sqrt{3} π b p - 3 a α =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2019 (03-May Shift-2)>Q 17

If a straight line passes through the point

(- 5, 4)

and makes an intercept of length

\frac{2}{\sqrt{5}}

between the lines

x + 2 y + 1 = 0

and

x + 2 y - 1 = 0,

then the equation of that line is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2021 (04-Aug Shift-1)>Q 18

If the vertices of a triangle

A B C

are

A (1, 7), B (- 5, - 1)

and

C (7, 4),

then the equation of a bisector of

A B C

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2021 (04-Aug Shift-2)>Q 19

For all

α, β \in R

and

α β > 0,

the line

α x + β y + \sqrt{α β} = 0

is such that it

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - The Straight Line>TS EAMCET 2020 (9-Sep Shift-1)>Q 20

If the family of straight lines

a x + b y + c = 0

, where

2 a + 3 b = 4 c

is concurrent at the point

P (l, m)

, then the foot of the perpendicular drawn from

P

to the line

x + y + 1 = 0

is