AP EAMCET · Maths · Straight Lines
A straight line \(L\) is perpendicular to the line \(5 x-y=1\) and the area of the triangle formed by the line \(L\) and the coordinate axes is 5 square units. The equation of the line \(L\) can be
- A \(x+5 y= \pm 2 \sqrt{2}\)
- B \(x+5 y= \pm 5 \sqrt{2}\)
- C \(x-5 y=5 \sqrt{2}\)
- D \(-x+5 y=3 \sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(x+5 y= \pm 5 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Slope of \(5x - y = 1\) is \(m_1 = 5\). Slope of line \(L\) is \(m_L = -\frac{1}{m_1} = -\frac{1}{5}\). Equation of line \(L\): \(y = -\frac{1}{5}x + c \implies x + 5y = 5c\). Let \(k = 5c\). Equation: \(x + 5y = k\). x-intercept: \(a = k\). y-intercept: \(b = \frac{k}{5}\).…
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