Question

if the straight line through the point P(3,4) make an angel π/6 with the X-axis and meets the line 3x+5y+1=0 at Q the length PQ is​

Answer 1

Answer:

eq. of line through P in parametric form

$\frac{x - 3}{ \cos(30) } = \frac{y - 4}{ \sin(30) } = r$

$x = 3 + r \cos(30) = \frac{ \sqrt{3}r }{2} + 3$

$y = 4 + r \sin(30) = 4 + \frac{r}{2}$

$3( \frac{ \sqrt{3} r}{2} + 3) + 5(4 + \frac{r}{2} ) + 1 = 0$

putting these x & y in 3x+5y+1=0

Step-by-step explanation:

$3 \sqrt{3} r + 18 + 40 + 5r + 2 = 0$

$(5 + 3 \sqrt{3} )r = 60$

$r = \frac{60}{3 \sqrt{3} + 5 }$

r is required distance