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Question

On shifting the origin to a particular point, the equation x2+y2−4x−6y−12=0 transforms to X2+Y2=K. Then K=

A
12
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B
25
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C
24
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D
5
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Solution

The correct option is B 25
Transformation of axis Let origin be shifted to (h, k), then

(x,y)=(Xh,Yk)

(Xh)2+(Yk)24(Xh)6(Yk)12=0

X2+Y22Xh4X2Yk6Y+h2+k2+4h+6k12=0

Comparing coefficients

2h=4

h=2

2k=6

k=3

h2+k2+4h+6k12=4+981812

=25

X2+Y2=K=25


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