Question

A straight line is drawn through the point P(√3,2), making an angle 30° with x-axis. Determine the length of the line measured from this point where it meets the line √3x-4y+8=0. Also find equation of the line through point P.​

Answer 1

Eq.of line thriugh p(root3,2) is:-

y-2=1/3^1/2.(x-3^1/2)

x-3^1/2=y.3^1/2–2.3^1/2

x-y.3^1/2=-3^1/2…………………(1)

3^1/2.x-4y=-8……………………..(2)

Multiply eq.(1)by 3^1/2 and subtract from eq(2).

-y=-5 => y=5

put y=5 in eq.(1)

x-5.3^1/3=-3^1/2

x=4.3^1/2 , Q(4.3^1/2, 5)

PQ=[(4.3^1/2–3^1/2)^2+(5–2)^2]^1/2

PQ=[27+9]^1/2=(36)^1/2= 6units