Question

Find the equations of the polar of the line
x + 셀 2+1
2+3 wo.t. the loincoid
2x² - y2 +32 22 in Symmetrical form
2​

Answer 1

Step-by-step explanation:

Answer

The lines should be x+y+z=0

and, 4x+y−2z=(−2)

Now, equation should lie on both planes.

So, the equation of line should be perpendicular to both planes.

Let the DRs of the line (a,b,c)

So, (a,b,c)⊥(1,1,1)

and, (a,b,c)⊥(4,,1,−2)

∴a+b+c=0

   4a+b−2c=0

On solving,

                 −2−1a=−2−4−b=1−4c

                 ⇒a=−3,b=6,c=−3

                 ⇒a=−1,b=2,c=−1

Let the coordinates of the point lying in xy plane (x,y,0)

on subtracting x+y=−1−(1)

and 4x+y=−2

⇒−3x=1

⇒x=3−1

Putting vbalue of x in (1)

3−1+y=−1

y=−1+3−1

   =