00:02
In this problem, we are given dou 2z by dou x square minus 5 times dou 2z by dou x dou y plus 6 times dou 2z by dou y square equals to 0.
00:23
Now, we have to make the transformation s is equals to y plus 2x, t is equals to y plus 3x.
00:34
So, first thing is that dou z by dou x can written as dou z over dou s into dou s over dou x plus dou z over dou t into dou t over dou x.
00:48
Now, dou s over dou x from here is 2 and dou t over dou x is 3.
00:58
So, from here we get dou by dou x is equals to 2 times dou by dou s plus 3 times dou by dou t.
01:08
Second thing is that dou z by dou y is nothing but dou z by dou s into dou s over dou y plus dou z over dou t into dou t over dou y.
01:24
Dou s over dou y and dou t over dou y from here is 1.
01:27
So, this simply is dou z over dou s plus dou z over dou t or we get dou by dou y is equals to dou by dou s plus dou y.
01:39
This is second main equation.
01:42
Now, next let us find what is dou 2z by dou x square.
01:47
This is nothing but dou by dou x of dou z over dou x.
01:52
Taking dou by dou x as this and dou z by dou x as this, this can be simply written as 4 times dou square z by dou s square plus 12 times dou square z by dou s dou t plus 9 times dou square z by dou t square.
02:19
Next, similarly i can write dou 2z by dou y square is dou by dou y of dou z over dou y.
02:27
So, we have dou by dou y here and dou z by dou y here.
02:32
So, this is simply dou square z by dou s square plus 2 times dou square z by dou s dou t plus dou square z by dou t square.
02:45
Similarly, we have dou square z by dou x dou y.
02:51
This is nothing but dou by dou x of dou z over dou y...