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AP EAMCET20227 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The curves y=x^2-1, y=8 x-x^2-9

Options

  1. Aintersect at right angles at (2,3)
  2. Btouch each other at (2,3)
  3. Cintersect at 45^
  4. Dintersect at 60^

Correct answer

B. touch each other at (2,3)

Step-by-step solution

y=x^2-1 y=8 x-x^2-9 For point of intersection, x^2-1=8 x-x^2-92 x^2-8 x+8=0 x^2-4 x+4=0 (x-2)^2=0 x=2 y=2^2-1=3 Point of intersection =(2,3) [ d y d x ]_ c₁ =2 x and [ d y d x ]_ c₂ =8-2 x At (2,3) , [ d y^ d x ]_ c₁ =4 and [ d y d x ]_ c₂ =4 aligned = & | [ d y d x ]_ c₁ - [ d y d x ]_ c₂ 1+ [ d y d x ]_ c₁ [ d y d x ]_ c₂ | & [ Angle between both curves ] aligned =0 Hence, both curves touch each other at (2,3) .

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