coordinate - set10 Q23

eqn of circle with center at origin is

x^2 +y^2 = r^2(radius square)

stmt1 : r^2 + s^2 =4 suff

stmt 2:
(v2, -v2) is this v^2, -v^2 or 2v,-2v, but in any case we dont know the radius & "v" here

so IMO ans should be A

if pt is (2,-2) then ans is D.

Hi,

Well the question is whether or not the data provided is sufficient to find out the value of r^2+s^2.

To know this you should know the equation of the circle.
equation of the circle is:
(x-h)^2+(y-k)^2= r^2

where:
(h,k) coordinates of the center of the circle in this case it is (0,0)
hence new equation is:
x^2+y^2= (radius)^2 ......eq 1
1) Using 1 radius is 2 and point on the circle is (r,s) so putting (r,s) in the new equation you get
r^2+s^2=4 hence 1 is sufficient to answer your question.
2) Using 2 we get
(v2)^2+(-v2)^2=(radius)^2
=> 2(V2)^2 = (radius)^2 ..eq2
since (r,s) also lie on the circle
r^2+s^2=(radius)^2 ..eq3
but from eq2 we know (radius)^2=2(V2)^2 substituting eq2 in eq3 we get
r^2+s^2=2(V2)^2

Here we see that there is still one variable v2 in the result.

So we can say answer is (a) that is 1 alone is sufficient to answer the question.

Hope this helps

Thanks
Komal
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Thanks to both of you...i get it now.