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Bunuel
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Bunuel
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.

The equation of Circle is -

\((x-h)^2 + (y-k)^2 = r^2\), where h & k are center of Circle.

Statement I:

The Circle passes through (0,0) & (0,7), We have -

\(r^2 = h^2 + k^2\) and \(r^2 = h^2 + (7-k)^2\). From these two equation, we have -

\(h^2 + k^2 = h^2 + (7-k)^2\)

\(k = 3.5\), But we can't find h. Hence, Insufficient.

Statement II:

Only radius is given So, Insufficient.

Combining the two we have -

\(k = 3.5, r = 5.\)

As the circle passes through (0,0)..

\(r^2 = h^2 + k^2\)

Here, h can be both positive and negative for given value of k & r.

Hence, Insufficient.

E.
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Bunuel
Where is the center of a circle on the xy plane?

(1) The circle passes through both the origin and (0,7).
(2) The diameter equals 10.


Suppose (x,y) is the centre of the circle. So the radius r can be defined as distance between the centre and any point on the circle.

So, x^2 +y^2 = x^2 + (y-7)^2 --> equation 1 from the statement 1. From this, we get the value of y.

From statement 2, diameter = 2r and since r^2 = x^2 +y^2 from statement 1 and we know the value of y, we can find x.

So, isn't C the answer? Correct me if I am wrong.

You can find X. But it can be both positive & negative.

Hence, E.
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