AP EAMCET2013MathematicsStraight Lines
If p and q are the perpendicular distances from the origin to the straight lines x -y cosec =a and x +y =a 2 , then
Options
- A4 p^2+q^2=a^2
- Bp^2+q^2=a^2
- Cp^2+2 q^2=a^2
- D4 p^2+q^2=2 a^2
Correct answer
A. 4 p^2+q^2=a^2
Step-by-step solution
Given equations of straight lines are aligned x -y cosec & =a x +y & =a 2 aligned Also, p= Perpendicular distance from the origin to the line (i) aligned & P= |0-0-a| ^2 + cosec ^2 = a 1 &=a = a 2 2 & 2 p=a 2 aligned and q= perpendicular distance from the origin to the line (ii) q= |0+0-a 2 | ^2 + ^2 = a 2 1 =a 2 Now, aligned 4 p^2+q^2 & =a^2 ^2 2 +a^2 ^2 2 & =a^2 ( ^2 2 + ^2 2 ) & =a^2(1)=a^2 aligned