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Find the Equation of the Straight Line Which Has Y-intercept Equal to 4 3 and is Perpendicular to 3x − 4y + 11 = 0. - Mathematics

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प्रश्न

Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.

संक्षेप में उत्तर

उत्तर

The line perpendicular to 3x − 4y + 11 = 0 is \[4x + 3y + \lambda = 0\]

It is given that the line

\[4x + 3y + \lambda = 0\]  has y-intercept equal to \[\frac{4}{3}\] 
This means that the line passes through \[\left( 0, \frac{4}{3} \right)\]

\[\therefore 0 + 4 + \lambda = 0\]

\[ \Rightarrow \lambda = - 4\]

Substituting the value of

\[\lambda\] , we get 

\[4x + 3y - 4 = 0\],which is equation of the required line.

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अध्याय 23: The straight lines - Exercise 23.12 [पृष्ठ ९३]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.12 | Q 10 | पृष्ठ ९३

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