The straight line through P x 1 , y 1 inclined at an angle θ with the x - axis meets the line a x + b y + c = 0 in Q . Find the length of P Q .

Given that the straight line through P x 1 , y 1 inclined at an angle θ with the x -axis meets the line a x + b y + c = 0 in Q . We need to find the length P Q . Let P Q = r . The equation of the line that passes through P x 1 , y 1 and makes an angle of θ with the x - axis is x - x 1 cos θ = y - y 1 sin θ = r . Then, the coordinates of Q are given by x = x 1 + r cos θ , y = y 1 + r sin θ Thus, the coordinates of Q are x 1 + r cos θ , y 1 + r sin θ . Clearly, Q lies on the line a x + b y + c = 0 . ∴ a x 1 + r cos θ + b y 1 + r sin θ + c = 0 ⇒ r = - a x 1 + b y 1 + c a cos θ + b sin θ ∴ P Q = a x 1 + b y 1 + c a cos θ + b sin θ

E M B I B E

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8

R D Sharma Solutions for Chapter: The Straight Lines, Exercise 8: EXERCISE 23.8

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: The Straight Lines, Exercise 8: EXERCISE 23.8

Attempt the practice questions on Chapter 23: The Straight Lines, Exercise 8: EXERCISE 23.8 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: The Straight Lines, Exercise 8: EXERCISE 23.8 with Hints & Solutions

MEDIUM

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 6

The straight line through $P (x_{1}, y_{1})$ inclined at an angle $∴ a (x_{1} + r \cos θ) + b (y_{1} + r \sin θ) + c = 0$ with the $x -$ axis meets the line $a x + b y + c = 0$ in $Q .$ Find the length of $\Rightarrow r = - \frac{a x_{1} + b y_{1} + c}{a \cos θ + b \sin θ}$ .

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 7

Find the distance of the point $A (2, 3)$ from the line $2 x - 3 y + 9 = 0$ measured along a line making an angle of $45^{0}$ with $x -$ axis.

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 8

Find the distance of the point $(3, 5)$ from the line $2 x + 3 y = 14$ measured parallel to a line having slope $1 / 2 .$

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 9

Find the distance of the point $(2, 5)$ from the line $3 x + y + 4 = 0$ measured parallel to a line having slope $3 / 4 .$

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 10

Find the distance of the point $(3, 5)$ from the line $2 x + 3 y = 14$ measured parallel to the line $x - 2 y = 1 .$

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 11

Find the distance of the point $(2, 5)$ from the line $3 x + y + 4 = 0$ measured parallel to the line $3 x - 4 y + 8 = 0 .$

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 12

Find the distance of the line $2 x + y = 3$ from the point $(- 1, - 3)$ in the direction of the line whose slope is $1 .$

HARD

11th CBSE

IMPORTANT

MATHEMATICS for CLASS XI>Chapter 23 - The Straight Lines>EXERCISE 23.8>Q 13

A line is such that its segment between the straight lines $5 x - y - 4 = 0$ and $3 x + 4 y - 4 = 0$ is bisected at the point $(1, 5) .$ Obtain its equation.

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