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I) The circle intersects with y axis at (0,2) and (0, -2) ---> No ifo about line k INSUFF
II) K intersects with axis at point (-3,0) ---> No info about circle ---> INSUFF

Together, K can't intercept and be on the same line. Answer is "No" SUFF

just because the circle intersects the y axis at 2 and -2 doesnt mean its center is at (0,0). Its center could be (5,0) or and (x,0) really. So it is possible for the line to intersect the center of the circle, but we cant be sure.

St1: We know that center of circle must be on the x-axis. But we don't know about line k.: INSUFF

St2: k intersect x-axis at (-3,0). No info about circle.: INSUFF

Together: Considering that center of circle will be on x-axis. Only line that can pass through (-3,0) and point (a,0) is x-axis. But we know that line k is not x-axis.: SUFF
_________________

There's an infinite number of circles that may pass thru 0,2 and 0,-2. The fact that k passes thru -3,0 does not help.

E

The answer E but for a different reason. if the circle intersects the Y axis at 0,-2 and 0,2 then y axis is the chord. Now any line which is perpendicular to it and bisecting it is the diameter (here the X axis). thus the center has to be of the form (a,0). Second statement says that K pass through (intersects X axis) at -3,0 => a = -3 ... hence insufficient. Both put together donot yeild the correct answer.

Stat1: with just stat1 we have no info abt line k, so insuff

Stat2: with just stat2 we have no info about the center of the circle, so insuff

even using stat1 we cannot say where the center of the circle is since the radius of the circle can vary, just one point on the line also does not give much more information since the slope of the line can vary, so stat 1& stat 2 doesnt help either...

There's an infinite number of circles that may pass thru 0,2 and 0,-2. The fact that k passes thru -3,0 does not help.

E

The answer E but for a different reason. if the circle intersects the Y axis at 0,-2 and 0,2 then y axis is the chord. Now any line which is perpendicular to it and bisecting it is the diameter (here the X axis). thus the center has to be of the form (a,0). Second statement says that K pass through (intersects X axis) at -3,0 => a = -3 ... hence insufficient. Both put together donot yeild the correct answer.