The power of (2,1) with respect to the circle 2 x 2 + 2 y 2 − 8 x − 6 y + k = 0 is positive if Options: A . &nbsp 0<k<12 B . &nbsp -12<k<12 C . &nbsp k>12 D . &nbsp k<12

Answer: Option C : C 2 x 2 + 2 y 2 − 8 x − 6 y + k = 0 ⇒ x 2 + y 2 − 4 x − 3 y + ( k 2 ) = 0 4 + 1 − 8 − 3 + k 2 > 0 k 2 − 6 > 0 → k > 12

The power of (2,1) with respect to the circle 2x2+2y2−8x−6y+k =

Question -

The power of (2,1) with respect to the circle $2 x^{2} + 2 y^{2} - 8 x - 6 y + k$ = 0 is positive if

Options:

A . 0<k<12

B . -12<k<12

C . k>12

D . k<12

Answer: Option C
:
C

$2 x^{2} + 2 y^{2} - 8 x - 6 y + k$ = 0

$\Rightarrow x^{2} + y^{2} - 4 x - 3 y + (\frac{k}{2})$ = 0

$4 + 1 - 8 - 3 + \frac{k}{2} > 0$

$\frac{k}{2} - 6 > 0 \to k > 12$

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