Check whether the following sequences are in A.P or not? `x+3,2x+4,3x+5,… `

Answer

A

Explanation

Let theslope of the chord through point (7,1) be m. Thus, equation of line is
`y -1 = m(x-7)`
or `mx -y +1 -7m =0`
Perpendicular distanc from `(0,0) =(r )/(2)`
`rArr (|7-1|)/(sqrt(1+m^(2)))=5`
`rArr (7m -1)^(2) = 25 (1+m^(2))`
`rArr49m^(2) -14m +1 = 25 +25m^(2)`
`rArr 24 m^(2) -14m -24 =0`
`rArr m_(1)m_(2) =-1`