Transform the equation 3 x + y + 10 = 0 into slope-intercept form, intercept form and normal form.

Given equation 3 x + y + 10 = 0 ⇒ y = - 3 x - 10 is the slope intercept form of the given equation of line. Given equation 3 x + y + 10 = 0 ⇒ - 3 x - y = 10 ⇒ - 3 x 10 - y 10 = 1 ⇒ x - 10 3 + y - 10 = 1 is the intercept form of the given equation of line. Given equation 3 x + y + 10 = 0 Dividing with 3 2 + 1 2 = 3 + 1 = 2 ⇒ - 3 2 x + - 1 2 y = 10 2 ⇒ x cos 7 π 6 + y sin 7 π 6 = 5 is the normal form of the given equation of line.

A straight line passing through A ( - 2 , 1 ) makes an angle of 30 ° with O X ↔ in the positive direction. Find the points on the straight line whose distance from A is 4 units.

Let, x 1 , y 1 = A ( - 2 , 1 ) , r = 4 and α = 30 ° Then, cos α = cos 30 ° = 3 2 , sin α = sin 30 ° = 1 2 Co-ordinates of point at a distance r from x 1 , y 1 on the given line are x 1 ± r cos α , y 1 ± r sin α . Co-ordinates of the required points are - 2 + 4 · 3 2 , 1 + 4 · 1 2 = - 2 + 2 3 , 3 and - 2 - 4 · 3 2 , 1 - 4 · 1 2 = - 2 - 2 3 , - 1 .

E M B I B E

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Earn 100

Transform the equation $x + y + 2 = 0$ into slope-intercept form, intercept form and normal form.

Important Questions on The Straight Line

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

Transform the equation

x + y - 2 = 0

into slope-intercept form, intercept form and normal form.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

Transform the equation

\sqrt{3} x + y + 10 = 0

into slope-intercept form, intercept form and normal form.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

If the product of the intercepts made by the straight line

x \tan α + y \sec α = 1 (0 \leq α < \frac{π}{2})

on the coordinate axes is equal to

\sin α,

find

α

.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

If the sum of the reciprocals of the intercepts made by a variable straight line on the axes of coordinates is a constant, then prove that the line always passes through a fixed point.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 3 - The Straight Line>Exercise 3(b)>Q II

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