AP EAMCET · Maths · Straight Lines
The point \(P(a, b)\) lies on the straight line \(3 x+2 y=13\) and the point \(Q(b, a)\) lies on the straight line \(4 x-y=5\). Then the equation of the line \(P Q\) is
- A \(x+y=7\)
- B \(x+y=5\)
- C \(x+y=2\)
- D \(x+y=21\)
Answer & Solution
Correct Answer
(B) \(x+y=5\)
Step-by-step Solution
Detailed explanation
\(3a + 2b = 13\) \(4b - a = 5 \implies a = 4b - 5\) \(3(4b - 5) + 2b = 13\) \(12b - 15 + 2b = 13\) \(14b = 28 \implies b = 2\) \(a = 4(2) - 5 = 3\) \(P = (3, 2)\), \(Q = (2, 3)\) \(m = \frac{3-2}{2-3} = \frac{1}{-1} = -1\) \(y - 2 = -1(x - 3)\) \(y - 2 = -x + 3\) \(x + y = 5\)
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