AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferentiationActual
If (x^2+y^2=t- 1 t ) and (x^4+y^4=t^2+ 1 t^2 ), then ( d y d x = )
Options
- A( 2 x^3 )
- B( 2 x^3 y )
- C( 1 x^3 )
- D( 1 x^3 y )
Correct answer
D. ( 1 x^3 y )
Step-by-step solution
Given, ( aligned & x^4+y^4=t^2+ 1 t^2 (i) & x^2+y^2=t- 1 t aligned ) On Squaring both sides, we get ( aligned x^4+y^4+2 x^2 y^2 & =t^2+ 1 t^2 -2 t^2+ 1 t^2 +2 x^2 y^2 & =t^2+ 1 t^2 -2 [ from Eq. (i) ] x^2 y^2 & =-1 y^2 & = -1 x^2 aligned ) Differentiating w.r.t. (x ), we get ( aligned 2 y y^ & = 2 x^3 y^ & = 1 x^3 y aligned ) ( ) Hence, answer is (d).