The locus of a point which moves such that the tangents from it to the two circles `x^(2)+y^(2)-5x-3=0` and `3x^(2)+3y^(2)+2x+4y-6=0` are equal, is given by

Options

A. `2x^(2)+2y^(2)+7x+4y-3=0`
B. `17x+4y+3=0`
C. `4x^(2)+4y^(2)-3x+4y-9=0`
D. `13x-4y+15=0`

Answer

B

Explanation

Let P(h, k) be the coordinates of a point from which equal tangents are drawn to the circles
`x^(2)+y^(2)-5x-3=0` and `3x^(2)+3y^(2)+2x+4y-6=0`. Then,
`h^(2)+k^(2)-5h-3=h^(2)+k^(2)+(2)/(3)h+(4)/(3)k-2`
`rArr 17h + 4+3=0`.
Hence, the locus of (h, k) is `17x+4y+3=0`.
`ul("ALITER")` Required locus is the radical axis of the given circles and its equation is given by
`S_(1)-S_(2)=0`
`rArr (x^(2)+y^(2)-5x-3)-(x^(2)+y^(2)+(2)/(3)x+(4)/(3)y-2)=0`
`rArr 17x+4y+3=0`