If the distance of the point (2,3) from the line 2x−3y+9=0 measured along a line x−y+1=0 is k units, then the value of k2 is
A
32
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B
32.00
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C
32.0
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Solution
The slope of the line x−y+1=0 is 1. So, it makes an angle of 45∘ with x−axis.
Equation of the line passing through (2,3) and making an angle of 45∘ is x−2cos45∘=y−3sin45∘=r
Coordinates of any point on this line are (2+rcos45∘,3+rsin45∘)≡(2+r√2,3+r√2)
If this point lies on the line 2x−3y+9=0, then 4+√2r−9−3r√2+9=0 ⇒r=4√2⇒k=4√2∴k2=32