reduce the equation x+y-root 2 =0 to the normal form x cos alpha +y sin alpha = p and hence - Maths - Straight Lines

Question

reduce the equation x+y-root 2 =0 to the normal form x cos alpha +y
sin alpha = p and hence find values of alpha and p

Manbar Singh · Accepted Answer

The given equation is,    x + y - 2 = 0⇒x + y = 2⇒x12 + 12 + y12 + 12 = 212 + 12⇒x2 + y2 = 1So, we get cos α = 12 and sin α = 12  and p =1Since, cos α > 0  and sin α > 0, so α lies in first quadrant
Now, sin αcos α = 1/21/2 ⇒tan α = 1⇒α = 45°So, given equation in normal form is,x cos 45° + y sin 45° = 1

reduce the equation x+y-root 2 =0 to the normal form x cos alpha +y sin alpha = p and hence find values of alpha and p