Let the tangent to the cubic curve x 3 + y 3 = a 3 at P ( x 1 , y 1 ) meets the curve again at Q ( h , k ) . Put A = x 1 h and B = y 1 k . Which of the following is true

Question

Let the tangent to the cubic curve x 3 + y 3 = a 3 at P ( x 1 ​ , y 1 ​ ) meets the curve again at Q ( h , k ) . Put A = x 1 ​ h ​ and B = y 1 ​ k ​ . Which of the following is true

TestHub · Accepted Answer

As above, A = 1 + x 1 3 ​ − y 1 3 ​ 3 y 1 3 ​ ​ and B = 1 − x 1 3 ​ − y 1 3 ​ 3 x 1 3 ​ ​ ⇒ A + B = 2 + x 1 3 ​ − y 1 3 ​ 3 ( y 1 3 ​ − x 1 3 ​ ) ​ = 2 − 3 = − 1 Putting A + B = − 1 in option (C): ( − 1 ) 2 − A B ( − 1 ) − A B − 1 = 1 + A B − A B − 1 = 0

Mathematics - Application of Derivative Question with Solution | TestHub

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