Question:
The straight line \( ax + by + c = 0 \) passes through the point \( (-10,7) \). If the line is perpendicular to \( 11x - 7y = 13 \), then the value of \( c \) is equal to
The straight line \( ax + by + c = 0 \) passes through the point \( (-10,7) \). If the line is perpendicular to \( 11x - 7y = 13 \), then the value of \( c \) is equal to
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For perpendicular lines: \( m_1 m_2 = -1 \).
Updated On: Apr 21, 2026
- \(8 \)
- \(-7 \)
- \(13 \)
- \(-13 \)
- \(5 \)
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The Correct Option is B
Solution and Explanation
Concept:
Product of slopes of perpendicular lines = \(-1\).
Step 1: Slope of given line.
\[ 11x - 7y = 13 \Rightarrow y = \frac{11}{7}x - \frac{13}{7} \] \[ m_1 = \frac{11}{7} \]
Step 2: Slope of required line.
\[ m_2 = -\frac{7}{11} \]
Step 3: Equation through point.
\[ y - 7 = -\frac{7}{11}(x + 10) \] \[ 11y - 77 = -7x - 70 \] \[ 7x + 11y - 7 = 0 \]
Step 4: Value of \( c \).
\[ c = -7 \]
Step 1: Slope of given line.
\[ 11x - 7y = 13 \Rightarrow y = \frac{11}{7}x - \frac{13}{7} \] \[ m_1 = \frac{11}{7} \]
Step 2: Slope of required line.
\[ m_2 = -\frac{7}{11} \]
Step 3: Equation through point.
\[ y - 7 = -\frac{7}{11}(x + 10) \] \[ 11y - 77 = -7x - 70 \] \[ 7x + 11y - 7 = 0 \]
Step 4: Value of \( c \).
\[ c = -7 \]
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