reduce the equation x+ root 3 y -4=0 to the normal form x cos alpha +y sin alpha = p - Maths - Straight Lines

Question

reduce the equation x+ root 3 y -4=0 to the normal form x cos alpha
+y sin alpha = p and hence find the values of alpha and p

Manbar Singh · Accepted Answer

The given equation is,    x + 3y - 4 = 0⇒x + 3y = 4⇒x12 + 32 + 3y12 + 32 = 412 + 32⇒x2 + 32y = 42⇒x2 + 32y = 2So, we get cos α = 12 and sin α = 32  and p = 2Since, cos α > 0  and sin α > 0, so α lies in first quadrant
Now, sin αcos α = 3/21/2 ⇒tan α = 3⇒α = 60°So, given equation in normal form is,x cos 60° + y sin 60° = 2

reduce the equation x+ root 3 y -4=0 to the normal form x cos alpha +y sin alpha = p and hence find the values of alpha and p