KVPY SX SB Exam 2015 Question Paper

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Question : 4 of 120

Marks: +1, -0

Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola

y = x^2

. Then C must lie on the curve -

$y = x ^2 + 2$
$y = 2x^2 + 1$
$y = - x^ 2 + 2$
$y = - 2x^2 + 1$

Solution:

∵ OB ⊥ OA
So,

t_1t_2 =-1

Now

h/2={t_1+t_2 }/2

t_1 + t_2 = h

…(1)
also

t^2_1 + t ^2_2= k

(t_1 + t_2)^2-2t_1t_2 = k

h^2 + 2 = k

locus is

x^2 + 2 = y

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