AP EAMCET · Maths · Pair of Lines
The distance between the lines represented by \(x^2+2 x y+y^2-8 m x-8 m y-9 m^2=0\) is
- A \(2 \sqrt{5} m\)
- B \(0\)
- C \(\frac{5 m}{\sqrt{2}}\)
- D \(5 \sqrt{2} \mathrm{~m}\)
Answer & Solution
Correct Answer
(D) \(5 \sqrt{2} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
\((x+y)^2 - 8m(x+y) - 9m^2 = 0\) Let \(Z = x+y\). \(Z^2 - 8mZ - 9m^2 = 0\) \((Z - 9m)(Z + m) = 0\) \(Z = 9m \text{ or } Z = -m\) \(x+y-9m = 0 \text{ and } x+y+m = 0\) \(d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}\) \(d = \frac{|-9m - m|}{\sqrt{1^2 + 1^2}}\)…
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