persamaan garis singgung elips 3x^ + 4y^ - 6x + 8y - 45 = 0 di titik (-3, -2) adalah... a. 3x + y + 11 = 0 b. 3x -y + 7 + 0 c. 3x - 2y + 5 = 0 d. x + 3y + 9 = 0

[tex]3x^2+4y^2-6x+8y-45=0 \\ 3x^2-6x+4y^2+8y-45=0 \\ 3(x^2-2x+1)+4(y^2+2y+1)-45=3+4 \\ 3(x-1)^2+4(y+1)^2=52 \\ $Garis singgung$ \\ 3(x-1)(x_1-1)+4(y+1)(y_1+1)=52 \\ 3(x-1)(-3-1)+4(y+1)(-2+1)=52 \\ -12(x-1)-4(y+1)=52 \\ 3(x-1)+y+1=-13 \\ 3x-3+y+1=-13 \\ 3x+y+11=0[/tex]

3x²+4x²-6x+8y-45=0 , (-3,-2)
menggunakn cara cepat:
3x1x +4y1y -3(x1+x) +4(y1+y) -45 = 0
3(-3)x +4(-2)y - 3(-3+x) +4(-2+y)-45 =0
-9x -8y+9 - 3x -8+4y-45 =0
-9x-3x -8y +4y +9-8-45 = 0
-12x-4y -44 = 0  :4
-3x - y -11 =0
=3x +y +11 = 0 (a)