If P is a variable point which is at a distance of 2 units from the line 2 x-3 y+1=0 and \sqrt{13} units from the point (5,6), then the equation of the locus of P is [AP EAPCET 21 May 2025 S2]

Correct Answer is : 12xy−5y2−44x−42y+243=0

4 x^2+12 x y-5 y^2-44 x-42 y+245=0

8 x^2+12 x y-5 y^2-44 x-42 y+243=0

Straight Lines and Pair of Straight Lines

Section: Mathematics

Question : 36 of 81

Marks: +1, -0

If P is a variable point which is at a distance of 2 units from the line 2x−3y+1=0 and √13 units from the point (5,6), then the equation of the locus of P is

[AP EAPCET 21 May 2025 S2]

4x2+12xy−5y2−44x−42y+245=0
12xy−5y2−44x−42y+243=0
8x2+12xy−5y2−44x−42y+243=0
12xy−13y2−44x−42y+245=0

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