If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 in four points (x_i, y_i) , for i=1,2,3 and 4 , then y_1+y_2+y_3+y_4 equals

Correct answer: A. 0 Given, array rlrl Given, & & x^2 y^2 & =c^4 & y^2(a^2-y^2) & =c^4 & y^4-a^2 y^2+c^4 & =0 array Let y_1, y_2, y_3 and y_4 are the roots. y_1+y_2+y_3+y_4=0

JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Hyperbola

JEE Main · Mathematics · Hyperbola

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 in four...

If the circle

x^2+y^2=a^2

intersects the hyperbola

x y=c^2

in four points \left(x_i, y_i\right)

, for

i=1,2,3

and 4 , then

y_1+y_2+y_3+y_4

equals

Options

A0
B $c$
C $a$
D $c^4$

Correct answer

A. 0

Step-by-step solution

Given,

\begin{array}{rlrl} \text { Given, } & & x^2 y^2 & =c^4 \\ \Rightarrow & y^2\left(a^2-y^2\right) & =c^4 \\ \Rightarrow & y^4-a^2 y^2+c^4 & =0 \end{array}

Let

y_1, y_2, y_3

and

y_4

are the roots. $\therefore \quad y_1+y_2+y_3+y_4=0

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