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Home » 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.
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.
CBSE | Class 11 | Exercise 23.6 | Maths | RD Sharma | Straight Lines
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.

Given:

Intercepts cut off on the coordinate axes by the line

    \[~ax\text{ }+\text{ }by\text{ }+8\text{ }=\text{ }0\text{ }\ldots \ldots \text{ }\left( i \right)\]

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

    \[2x\text{ }\text{ }3y\text{ }+6\text{ }=\text{ }0\text{ }\ldots \ldots \left( ii \right)\]

Since , the slope of two lines is equal

The slope of the line (i) is:

    \[~a/b\]

The slope of the line (ii) is:

    \[2/3\]

On equating,

    \[-a/b\text{ }=\text{ }2/3\]

    \[a\text{ }=\text{ }-2b/3\]

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

On 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

given,

    \[{{d}_{1}}~=\text{ }{{d}_{2}}\]

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

    \[b\text{ }=\text{ }4\]

hence ,

    \[a\text{ }=\text{ }-2b/3\]

    \[=\text{ }-8/3\]

∴ The value of

a is

    \[-8/3\]

and

    \[b\text{ }is\text{ }4.\]

i

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