Line `x/a+y/b=1` cuts the coordinate axes at `A(a ,0)a n dB(0,b)` and the line `x/a^(prime)+y/b^(prime)=-1` at `A (-a ,)` and `B^(prime)(0,-b^(prime))dot` If the points `A ,B ,A^(prime),B '` are concyclic, then the orthocentre of triangle `A B A '` is `(0,0)` (b) `(0,b^(prime))` `(0,(a a^(prime))/b)` (d) `(0,(bb^(prime))/a)`

Options

A. `(0, 0)`
B. `(0, b')`
C. `(0, (aa')/(b))`
D. `(0, (b b')/(a))`

Answer

B, C

Explanation

If `A, B, A', B'` are concyclic then
`rArr (OA)(OA') = (OB)(OB')`
`rArr -b b' = -aa'`
For `DeltaABA'` orthocenter lies on the `OB`
`:.` Let the co-odinate of orthocentre is `H(0,k)` then
Slope of `A'H rArr ((k)/(a'))`
Slope of `AB rArr (-(b)/(a))`
`:. ((k)/(a'))(-(b)/(a)) = -1`
`:.` co-ordinate of orthocenter are `(0, b')(0, (a a')/(b))`