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Equation of tangent to circle x 2 +y 2 -2x-4y-4=0 and parallel to the line 3x+4y=0 is????

Equation of tangent to circle x2+y2-2x-4y-4=0 and parallel to the line 3x+4y=0 is????

Grade:11

1 Answers

kkbisht
90 Points
5 years ago
circle :x2+y2-2x-4y-4=0
Centre: (1,2)ย  ย  radius :ย \sqrt{}1+4+4 = 3
Let the equationย  of the tangent is : y=mx+c
as the tangent is parallel to the line 3x+4y=0 => m=-3/4
Therefore the tangent is 4y+3x-4c=0
Length of perpendicular from centre( 1,2) to the tangent 4y+3x-4c=0ย  must be equal to radius= 3
ie.ย  ย ( 4.2+3.1-4c)/\sqrt{}42 +32ย = 3ย  ย =. 8+3-4c=5.3=15 ==>c= -1
Therefore Eqn of tangent is 4y+3x+4=0
By kkbisht

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