Application of Derivatives 2

Two curves C1 : y = x2 - 3 and C2 : y = kx2, k ε R intersect each other at two different points. The tangent drawn to C2 at one of the points of intersection A(a,y1), (a>0) meets C1 again at B (1, y2) (y1 ≠y2). The value of 'a' is
(A) 4
(B) 3
(C) 2
(D) 1

2 Answers

1357
Manish Shankar ·

B=(1,-2)
y1=ka2
Equation of line
y-y1x-a=2ka

it passes through B

So -2-ka2=(1-a)2ka

ka2-2ka-2=0

Also we have a2=3/(1-k)

1
Subhradeep Patra ·

but point B .. how is it (1,-2) ?

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