The locus of mid points of the segment intercepted between the axes by the line xseca + ytana = p is ……
(a) [p2/(4x2)] = 1 + [p2/(4y2)]
(b) (x2/p2) + (y2/p2) = 4
(c) (p2/x2) = 1 + (p2/y2)
(d) [p2/(4x2)] + [p2/(4y2)] = 1
The correct option (a) [p2/(4x2)] = 1 + [p2/(4y2)]
Explanation:
line: xsecα + ytanα = p
vertex p of vector AB : (x, y) = [{(pcosα)/2}, {(pcotα)/2}]
∴ secα = (p/2x) and tanα = (p/2y)
∵ sec2α – tan2α = 1
∴ (p2/4x2) – (p2/4y2) = 1
