﻿   Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes:  1. equal in magnitude but opposite in sign  2. such that their sum is 14 : Kaysons Education

# Find The Equation To The Straight Line Which Passes Through The Points (3, 4) And Having Intercepts On The Axes:  1. Equal In Magnitude But Opposite In Sign  2. Such That Their Sum Is 14

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## Question

### Solution

Correct option is

x – y + 1 = 0, 4x + 3y = 24 and x + y = 7

1. Let intercepts on the axes be a and –a respectively.

∴ The equation of the line in intercept form is

Since, eq. (i) passes through (3, 4), then

3 – 4 = a

∴     a = –1

From (i),

x – y + 1 = 0

which is the required equation of the line.

2. Let the equation of the line be

This passes through (3, 4)

Therefore,

It is given that a + b = 14

∴       b = 14 – a

Putting b = 14 – in (ii), we get

⇒   42 – 3a + 4a = 14a – a2

⇒   a2 – 13a + 42 = 0

⇒   (a – 7)(a – 6) = 0

∴    a = 6, 7

Then,

b = 8, 7                    (âˆµ b = 14 – a)

Hence the required equations are

i.e.,    4x + 3y = 24 and x + y = 7.

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