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
- A Not a Straight Line
- B A different Straight Line
- C Same as the straight line \(p=0\)
- D A Pair of straight lines
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 \(p+c q=0\):…
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