If the straight line drawn through the point P(√3,2) and making an angle π/2 with the x-axis meets the line √3x-4y+8=0 at Q then the length of PQ is

(a) 4

(b) 5

(c) 6

(d) none

Dear Harshit,

The equation of the line passing through the point P(√3,2) and making angle of 90 degrees with x axis nothig but the line line x= √3.

Now put this value of x in thegiven equation

we get  √3 * (√3) - 4y + 8 = 0

---> 4y = 11 ---> y = 11/4

so the point is Q( √3 , 11/4 )

Now distance between the points comes out to be |(11/4) - 2| = 3/2.

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