For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.

Asked by Aaryan | 2 years ago |  45

1 Answer

Solution :-

Given:

Intercepts cut off on the coordinate axes by the line ax + by +8 = 0 …… (i)

And are equal in length but opposite in sign to those cut off by the line

2x – 3y +6 = 0 ……(ii)

We know that, the slope of two lines is equal

The slope of the line (i) is \( \dfrac{-a}{b}\)

The slope of the line (ii) is \( \dfrac{2}{3}\)

So let us equate,

\( \dfrac{-a}{b}= \dfrac{2}{3}\)

a = \( \dfrac{-2b}{3}\)

The length of the perpendicular from the origin to the line (i) is

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 22

The length of the perpendicular from the origin to the line (ii) is

By using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 23

It is given that, d1 = d2

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 24

b = 4

So, a = \( \dfrac{-2b}{3}\)

\( \dfrac{-8}{3}\)

The value of a is \( \dfrac{-8}{3}\) and b is 4.

Answered by Aaryan | 2 years ago

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