1. if a straight line through the point P(3,4) make an angle 30 degrees with x-axis and meets the line 12x + 5y +10=0 at Q, find the lenghth of PQ.2. find X if (X,2) is an interior point of triangle ABC formed bylines A+B=4,3A-7B=8,4A-B=31.

Hello Ashwin,

Its a nice question you have posted.

Answer to Q no 1.

Generic Equation of a straight line :

 y- y1 = m(x -x1). For the question above , (x1,y1) = (3,4).  And slope is given to be m =tan 30 = 1/sqrt(3).

So the equation of line becomes :  y-4 = m(x-3) where m is as mentioned above.

Now the intersection point of two lines can be easily found out by just substituting value of y from one equation to another. Use value of sqrt(3) =1.732 and you the following intersection point:

Q= (-1.44,1.44)

From the two points P and Q

the distance PQ can be calculated as =  5.125

Hope this exaplanation solves your query. This question is just computational intensive.

Regards,

Ankit Jain

This question can easily be solved by using parametric eqn firstly find value of x and y in the form of r then put the values in the given eq