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Question

If the distance of the point (2,3) from the line 2x3y+9=0 measured along the line xy+1=0 is k units, then the value of k2 is

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Solution

Slope of the line xy+1=0 is 1
So angle made by the line in anticlockwise direction with +ve xaxis is 45
Now, parametric equation of the line having the slope as 1 and passing though (2,3) will be
x=2+rcos45; y=3+rsin45x=2+r2; y=3+r2

Now substituting the values of x,y in the line 2x3y+9=0
4+2r93r2+9=0r=42k=42k2=32

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