Question

the equation to the pair of tangents drawn from (3,2) to the circle x²+y²-6x+4y-2=0 is​

Answer 1

Answer:

6.

The equation to the pair of tangents drawn from(3,2) to the circle x2 + y2 - 6x + 4y-2=0 is

Answer 2

Answer:

The equation of pair of tangents drawn to circle is

$35x^{2}+15y^{2}+48xy+138x+84y+123=0$

Step-by-step explanation:

The equation of the given circle is $S=x^{2}+y^{2}-6x+4y-2=0$ and we are required to find the equation of pair of tangents drawn from the point (3,2)

The relation for pair of tangents drawn to a circle from the point $(x_{1},y_{1})$ is $S.S_{11}=S_{1}^{2}$ where

$S_{11}=x_{1}^{2}+y_{1}^{2}+2gx_{1}+2fy_{1}+c\\S_{1}=xx_{1}+yy_{1}+g(x+x_{1})+f(y+y_{1})+c$

Finding these equations for the given point,we get

$S_{11}=3^{2}+2^{2}-6(3)+4(2)-2=1\\S_{1}=3x+2y+3(x+3)+2(y+2)-2=6x+4y+11$

Substituting these values in our given relation,we get

$(x^{2}+y^{2}-6x+4y-2).(1)=(6x+4y+11)^{2}\\= > x^{2}+y^{2}-6x+4y-2=36x^{2}+16y^{2}+121+48xy+88y+132x\\= > 35x^{2}+15y^{2}+48xy+138x+84y+123=0$

Hence,

The equation of pair of tangents drawn to circle is

$35x^{2}+15y^{2}+48xy+138x+84y+123=0$

#SPJ2