If the area of the circle 4x2+4y2−8x+16y+k=0 is 9πsquare units, then the value of k is

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-16

±16

answer is C.

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Detailed Solution

We have,4x2+4y2−8x+16y+k=0⇒x2+y2−2x+4y+k4=0The radius of this circle is 1+4−k4=20−k2We have,Area of the circle = 9π square units⇒π20−k4=9π⇒k=−16

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