If The Two Lines x – A = 0 And y – B =  0 Are Conjugate W.r.t. The Hyperbolaxy = c2, Then The Locus Of (a, B) Is

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If the two lines x – a = 0 and y – b =  0 are conjugate w.r.t. the hyperbolaxy = c2, then the locus of (a, b) is


Correct option is

xy = 2c2

x – a = 0                                                        ……. (1)

y – b =  0                                                       ……. (2)

are conjugate w.r.t.

Let pole of (1) be (x1y1) w.r.t.                       ....... (3)

Then its polar is x1y + xy= 2c2                      …… (4)

Compare (1) and (4)


Now line (1) and (2) are conjugate and so pole of one line lies on the other line

⇒  (x1y1) lies on (2)         ⇒ y1 – b =0

∴ locus of (a, b) is xy = 2c2



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