TS EAMCET · Maths · Straight Lines
Let the line Ldrawn perpendicular to the lines \(2 x-3 y+4=0\) and \(6 x-9 y+7=0\) meet them at \(A\) and \(B\) respectively. If \(\mathrm{P}(1,1)\) is a point on \(\mathrm{L}\), then the ratio in which \(\mathrm{P}\) divides \(\mathrm{AB}\) is
- A \(9: 4\) internally
- B \(9: 4\) externally
- C \(4: 9\) internally
- D \(4: 9\) externally
Answer & Solution
Correct Answer
(B) \(9: 4\) externally
Step-by-step Solution
Detailed explanation
The lines are \(L_1: 2x-3y+4=0\) and \(L_2: 6x-9y+7=0\). Rewrite \(L_1\) with coefficients matching \(L_2\): \(3(2x-3y+4)=0 \implies 6x-9y+12=0\). Distance from \(\mathrm{P}(1,1)\) to \(L_1\): \(d_1 = \frac{|6(1)-9(1)+12|}{\sqrt{6^2+(-9)^2}} = \frac{|9|}{\sqrt{117}}\). Distance…
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