Normal at point (5$$, $$3) to the rectangular hyperbola xy – y – $$2x$$ – $$2$$ $$=$$ $$0$$ meets the curve at the point whose coordinates are

Question

Normal at point (5$$, $$3) to the rectangular hyperbola xy – y – $$2x$$ – $$2$$ $$=$$ $$0$$ meets the curve at the point whose coordinates are

Infinity Learn · Accepted Answer

Equation of the hyperbola can be written as (x$$ – $$1) (y$$ – $$2) $$=$$ $$4or$$ $$y=2+4x$$−$$1dydx=$$−$$4(x$$−$$1)2Any$$ point on the hyperbola is $$1+2t$$, $$2+2t=(5$$, $$3)$$⇒$$t=2So$$ slope of the normal at (5$$, $$3) is−$$dxdy(5$$, $$3)=4Equation$$ of the normal at (5$$, $$3) is y – $$3$$ $$=$$ $$4(x$$ – $$5)$$ which will pass $$through1+2t$$,$$2+2t$$ if $$2+2t=4(1+2t)$$−$$17$$⇒$$8t2$$−$$15t$$−$$2=0$$⇒$$t=2$$,−$$18$$.For $$t=$$−$$18$$, we get the required point $$as1$$−$$28$$, $$2$$−$$21/8=34$$,−$$14$$

Normal at point (5, 3) to the rectangular hyperbola $x y - y - 2 x - 2 = 0$
meets the curve at the point whose coordinates are

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Normal at point (5, 3) to the rectangular hyperbola xy – y – 2x – 2 = 0 meets the curve at the point whose coordinates are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Normal at point (5, 3) to the rectangular hyperbola $x y - y - 2 x - 2 = 0$
meets the curve at the point whose coordinates are