Question
Question: If the length of the perpendicular drawn from origin to the line whose intercepts on the axes are *a...
If the length of the perpendicular drawn from origin to the line whose intercepts on the axes are a and b be p, then
A
a2+b2=p2
B
a2+b2=p21
C
a21+b21=p22
D
a21+b21=p21
Answer
a21+b21=p21
Explanation
Solution
Equation of line is ax+by=1 ⇒ bx+ay−ab=0
Perpendicular distance from origin to given line is
p=a2+b2−ab ⇒ aba2+b2=p1 ⇒ a2b2a2+b2=p21
⇒ a21+b21=p21