The curves C 1 : y = x 2 − 3 ; C 2 : y = k x 2 , k 0 ) m

Question

The curves C 1 ​ : y = x 2 − 3 ; C 2 ​ : y = k x 2 , k < 1 intersect each other at two different points. The tangent drawn to C 2 ​ , at one of the points of intersection A = ( a , y 1 ​ ) ( a > 0 ) meets C 1 ​ again at B ( 1 , y 2 ​ ) . ( y 1 ​  = y 2 ​ ). Then value of a =

TestHub · Accepted Answer

Solving C 1 ​ and C 2 ​ ⇒ A ( 1 − k 3 ​ ​ , 1 − k 3 k ​ ) = ( a , k a 2 ) ≡ ( a , a 2 − 3 ) Tangent to C 2 ​ at A is y + a 2 − 3 = 2 k x ⇒ B = ( 1 , − 2 ) ( A  = 1 ) From expression (1) − 2 + a 2 − 3 = 2 a ( 1 − a 2 3 ​ ) ⇒ a = 3 , a = − 2 , a = 1 ∴ a = 3

Mathematics - Application of Derivative Question with Solution | TestHub

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