If the straight line passes through the point P(3,4)and makes the angle 30degree with the x-axis and meets the line 12x+5y=10 at Q then find the length of PQ

Dear Student

Equation of line passing through P(3,4) and having slope m=tan30° is given by
y – 4=tan30°(x-3)
y –4=(1/√3)(x-3)
√3(y-4)=x-3... .........(1)
Q is the intersection of this line with 12x+5y+10=0..........(2)
Solve (1) and (2) for x and y
we will get coordinates of Q.
since, coordinates od P as well as Q are known now
Now use distance formula to calculate PQ.
PQ will come around 5.11 units
Thanks