Question

if the straight line drawn through the point p(root 3 ,2) making an angle pi/6 with x axis meets the line root 3x- 4y+8=0 at q . then pq is

Answer 1

Answer:

6 units.

Step-by-step explanation:

Let us assume that the equation of the straight line is, y=mx +c. {Slope-intercept form}

Now, m = tan (π/6)= 1/√3 {Given}

So, the equation becomes y= x/√3 +c ..... (1)

This line (1), passes through point p(√3, 2).

Hence, 2=√3/√3 +c, ⇒c=1

Finally, the equation becomes y=x/√3 +1, ⇒x-√3y+√3=0  ..... (2)

Given, straight line (2) and the straight line √3x-4y+8 =0 ........ (3), intersect at point q.

Modify the equation (2), as √3x-3y+3 =0 ......(4)

Now, by {(4)-(3)}, we get, y-5 =0, ⇒y=5

Again, from equation (3), √3x-5×4+8=0, ⇒x=4√3

So, point q becomes (4√3, 5).

Hence, the distance pq= $\sqrt{(4\sqrt{3}-\sqrt{3}  )^{2}+(5-2)^{2}  }$

=$\sqrt{27+9}$= 6 units. (Answer)

Answer 2

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