Find the values of k for which the line `(k-3)x-(4-k^2)` `y+k^2-7k+6=0` is (a) Parallel to the xaxis, (b) Parallel to the vaxis, (c) Passing through the origin.

Explanation

Given equation of line is,
`(k-3)x-(4-k^(2))y+(k^(2)-7k+6)=0`
`(i)` If line is parallel to `x`-axis, then
`"coefficient of " x=0`
`implies k-3=0implies k=3`
`(ii)` If line is parallel to `y`-axis, then
coefficient of `y=0`
`implies (4-k^(2))=0implies k^(2)=4`
`implies k=+-2`
`(iii)` If line passes through the origin then
constant term`=0`
`implies k^(2)-7k+6=0`
`implies (k-1)(k-6)=0`
`implies k=1` or `k=6`