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AP EAMCET · Maths · Straight Lines

If \(p=a_1 x+b_1 y+k_1=0, q=a_2 x+b_2 y+k_2=0\) and \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{k_1}{k_2}\), then the curve \(p+c q\) is

  1. A Not a Straight Line
  2. B A different Straight Line
  3. C Same as the straight line \(p=0\)
  4. D A Pair of straight lines
Verified Solution

Answer & Solution

Correct Answer

(C) Same as the straight line \(p=0\)

Step-by-step Solution

Detailed explanation

Given \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{k_1}{k_2}=\lambda\). Substitute \(a_1=\lambda a_2, b_1=\lambda b_2, k_1=\lambda k_2\) into \(p\): \(p=\lambda a_2 x+\lambda b_2 y+\lambda k_2 = \lambda(a_2 x+b_2 y+k_2) = \lambda q\). Substitute \(p=\lambda q\) into \(p+c q=0\):…