 Hello friends, let's discuss the following question. It says find the value of k for which the line k minus 3x minus 4 minus k square y plus k square minus 7k plus 6 is equal to 0 is a parallel to x axis v parallel to y axis c passing through origin. So we have to find the value of k in these three cases. Let us now move on to the solution and let us discuss the case one when line is parallel to x axis. When line is parallel to x axis then the coefficient of x is 0 because this is the line which is parallel to x axis and here say this distance is a. So this is the line y is equal to a and here the coefficient of x is 0. So this implies coefficient of x. So the given line to x minus 4 minus k square y plus k square minus 7k plus 6 is equal to 0 is parallel to x axis. This implies coefficient of x is 0 that is k minus 3 is equal to 0 and this implies k is equal to 3. Let us now discuss the second case when line is parallel to y axis. When line is parallel to y axis then the coefficient of y is 0 because if this distance is a then this is the line x is equal to a and here coefficient of y is 0. Now in this line coefficient of y is minus 4 minus k square and this is equal to 0 and this implies 4 minus k square is equal to 0 which again implies k square is equal to 4 and this implies k is equal to plus minus 2. Let us now discuss the case when line passing through origin. So if line passes through the origin the 0.00 satisfies the equation of line that is x is equal to 0, y is equal to 0 satisfies the equation of the line. So the given line k minus 3x minus 4 minus k square y plus k square minus 7k plus 6 is equal to 0 passes through origin that is it passes from 0 0. So this implies the 0.00 satisfies this equation so we have k minus 3 into 0 minus 4 minus k square into 0 plus k square minus 7k plus 6 is equal to 0 and this implies k square minus 7k plus 6 is equal to 0. Now we solve this quadratic equation for k. Let us now factorize this equation so it is k square minus 6k minus k plus 6 is equal to 0 taking k common from first two terms we have k into k minus 6 and taking minus 1 common from the last two terms we have minus 1 into k minus 6 is equal to 0. Now taking k minus 6 common we have k minus 6 into k minus 1 is equal to 0 and this implies k is equal to 6 or k is equal to 1. Hence in first case when line is parallel to x axis k is equal to 3 and in the second case when line is parallel to y axis k is equal to plus minus 2 and in the third case when line passes through origin k is equal to 6 or 1. So that is all for this session. Goodbye and take care.