$$x = r cos \Theta$$ $$y = r sin \Theta$$

Now, by substituting in $$L_{1}$$, we get

$$\frac{1}{OA} = \frac{sin\Theta – cos\Theta }{10}$$

Now, by substituting in $$L_{2}$$, we get

$$\frac{1}{OB} = \frac{sin\Theta – cos\Theta }{20}$$ $$h = r cos \Theta$$ $$k = r sin \Theta$$

Therefore, $$\frac{2}{r} = \frac{sin\Theta – cos\Theta }{10} + \frac{sin\Theta – cos\Theta }{20}$$

= 40 = $$3(r sin \Theta ) – 3 (r cos \Theta )$$

= 3y – 3x = 40

Therefore, the Locus Of P Is 3y – 3x = 40

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