# Math Questions Ans a Ans d

• anyone attempting the above ??

•   plz help with this one .

• man111 singh ·

Not sure.....

(1) if we take u = (1,0,0) , v = (1/2 , 1, 0 ) and w = (1/2 ,1/2 ,1/2). the relation is not true

(2) Ratio as 1:1:1

(3) d = 1

• @man111 - plz explain Q 2 and 3 .

• rishabh ·

2) consider the figure,
in triangle BOC,
OBC = 90-c , OCB = 90-B
=> BOC = B+c
by using sine rule,
RÎ”BOc = BC2sin(BOC) = a2sin(B+c) = circumradius of Î”ABC
similarly others also = R (of Î”ABC)

.:. ratio = 1:1:1

• thanks rishabh and man111

• d=2 is right

but why hyperbola only of the form xy =k ??

• rishabh ·

3)we can notice that x=y will be the only solution for both hyperbola and circle when it is of the form xy=k and too the circle will just fit in between the 2 branches of the hyperbola
(can be understood from a diagram)

so the hyperbola is xy=1 {as b=0 and given that c=a}
so now on solving we get d=2

• rishabh ·

deleted my earlier post and posted new one.

• rishabh ·

if it were any other hyperbola,
case-1
for both points of intersection to lie on a straight line (y=x in this case)
only other possibility would be that the points of intersection lie on x-axis or y-axis. so this is not considered.

case-2
in any other case there will be 4 solutions will can't lie on straight line

• hmmm . understood what you meant to say .

thanks rishabh .

• man111 singh ·

Thanks Rishabh for Nice explanation

I also confused in that question.

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