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Question

The equation of the tangent from the point 0,1 to the circle x2+y2-2x-6y+6=0, is


A

3x2-y2+4xy-4x-6y+3=0

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B

3y2+4xy-4x-6y+3=0

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C

3x2+4xy-4x-6y+3=0

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D

3x2+y2+4xy-4x-6y+3=0

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Solution

The correct option is B

3y2+4xy-4x-6y+3=0


Explanation for the correct option

Given circle is x2+y2-2x-6y+6=0 and given point is 0,1
So, x1=0,y1=1

The equation of pairs of tangents to the circle x2+y2+2gx+2fy+c=0 from a point x1,y1 is given as,
x2+y2+2gx+2fy+cx12+y12+2gx1+2fy1+c=x·x1+y·y1+gx+x1+fy+y1+c2(1)

Comparing the given equation to the x2+y2+2gx+2fy+c=0 form of circle, we see that,
2gx=-2xg=-12fy=-6yf=-3c=6

Substituting the values in (1),
x2+y2+2-1x+2-3y+602+12+2-10+2-31+6=0·x+1·y+-1x+0+-3y+1+62x2+y2-2x-6y+60+1+0-6+6=y-x-3y-3+62x2+y2-2x-6y+61=-x-2y+32x2+y2-2x-6y+6=x2+4y2+9+4xy-6x-12ya+b+c2=a2+b2+c2+2ab+2bc+2cax2+y2-2x-6y+6=x2+4y2+4xy-6x-12y+93y2+4xy-4x-6y+3=0

Therefore, the equation of the pair of tangents is 3y2+4xy-4x-6y+3=0

Hence, option(B) i.e. 3y2+4xy-4x-6y+3=0 is correct.


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