AP EAMCET · Maths · Straight Lines
If \(\left(x_1, y_1\right)\) and \(\left(x_2, y_2\right)\) are two points on the line \(x+y+3=0\) such that each of them is at a distance of \(\sqrt{5}\) units from the line \(x+2 y+2=0\), then
- A -6
- B 20
- C 6
- D -20
Answer & Solution
Correct Answer
(A) -6
Step-by-step Solution
Detailed explanation
Line equation: \( y = -x-3 \) Distance condition: \( \frac{|x+2y+2|}{\sqrt{1^2+2^2}} = \sqrt{5} \) \( |x+2(-x-3)+2| = 5 \) \( |-x-4| = 5 \) \( -x-4 = 5 \Rightarrow x_1=-9, y_1=-(-9)-3=6 \) \( -x-4 = -5 \Rightarrow x_2=1, y_2=-(1)-3=-4 \) Sum of coordinates:…
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