straight line

Line L has intercepts a and b on the axes,the axes are rotated thru a certain angle,now the intercepts are p and q , then

A)a²+b² = p²+q²
B)1/a² + 1/b² = 1/p² + 1/q²
C)a²+p² = b²+q²
D)1/a² + 1/p² = 1/b² + 1/q²

2 Answers

Well... what remains constant here is distance from origin...

initially line was x/a+y/b=1
d_{from 0,0}=1/|1/a²+1/b²| ..(i)

finally after rotation eqn is say

X/p+Y/q=1
d_{from 0,0}=1/|1/p²+1/q²| ..(ii)

from (i) and (ii)

1/a²+1/b²=1/p²+1/q²
option (B)

ok,thx priyam

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