AP EAMCET · Maths · Straight Lines
The points \((2,3)\) and \(\left(-4,-\frac{4}{3}\right)\) lie on the opposite sides of the line \(\mathrm{L} \equiv 5 \mathrm{x}-6 \mathrm{y}+\mathrm{k}=0\) and k is an integer. If the points \((1,2)\) and \((4,5)\) lie on the same side of the line \(\mathrm{L}=0\), then the perpendicular distance from origin to the line \(\mathrm{L}=0\) is
- A \(\frac{7}{\sqrt{61}}\)
- B \(\frac{9}{\sqrt{61}}\)
- C \(\frac{10}{\sqrt{61}}\)
- D \(\frac{11}{\sqrt{61}}\)
Answer & Solution
Correct Answer
(D) \(\frac{11}{\sqrt{61}}\)
Step-by-step Solution
Detailed explanation
\((5(2)-6(3)+k)\left(5(-4)-6\left(-\frac{4}{3}\right)+k\right)\((5(1)-6(2)+k)(5(4)-6(5)+k)>0 \implies (k-7)(k-10)>0 \implies k10\) Combining the conditions and knowing \(k\) is an integer: \(10Perpendicular distance from origin \((0,0)\) to \(5x-6y+11=0\):…
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