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Question

The number of lines that can be drawn through the point (4,5) at distance of 12 units from the point (2,3) is

A
0
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B
1
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C
2
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D
infinite
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Solution

The correct option is A 0
Let line through Point(4,5) with slope m
y+5=mx4m
mxy(4m+5)=0
Distance of above equation from point (2,3) is 12

2m34m5m2+1=12

6m8m2+1=12

3m4m2+1=6

3m+4m2+1=6
On squaring both sides

9m2+16+24mm2+1=36

9m2+16+24m=36m2+36

27m224m+20=0

m=24±576216054

m=24±158454

m has imaginary roots
Hence No such line is possible


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