Check whether the following sequences are in A.P or not? `z-1,z-3,z-5...`

Answer

B

Explanation

AB subtends right angle at P and Q on variable line.

So, AB is a diameter of circle whose chord is a variable line. Equation of circle is:
`x (x-6) +y xx y =0`
or `x^(2) +y^(2) -6x =0` (i)
Equation of line through (2,4) is:
`y-4 =m(x-2)`
or `y = mx +(4-2m)` (ii)
Line (ii) is a chord if `|(3m+(4-2m))/(sqrt(1+m^(2)))| lt3`
`rArr 8m^(2) - 8m - 7 gt 0`
`m in (-oo,(2-3sqrt(2))/(4))uu((2+3sqrt(2))/(4),oo)`