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Question

The two circles x2+y2−2x+22y+5=0 and x2+y2+14x+6y+k=0 intersect orthogonally provided k is equal to ?

A
47
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B
47
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C
49
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D
49
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Solution

The correct option is A 47

If 2 circles cut each other orthogonally then

d2=r12+r22 where d is the distance between the centers

C1=(1,11), r1=12+1125=117

C2=(7,3), r2=72+32k=58k

(C1C2)2=r12+r22

82+82=117+58k

129=175k

k=47


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