Answer:
See the works below.
Step-by-step explanation:
One of the way to check if a linear line is tangent to a circle:
Substitute the linear equation to the circle's equation,
- If the Discriminant (D) = 0, then it is tangent to the circle.
- If the Discriminant (D) < 0, then it is outside to the circle.
- If the Discriminant (D) > 0, then it intersects with the circle.
Linear's Equation:
[tex]3x - y + 8 =0[/tex]
[tex]y=3x+8[/tex]
Now, we substitute the y in the Circle's Equation with (3x + 8):
[tex]x^2+y^2-18x-10y+16=0[/tex]
[tex]x^2+(3x+8)^2-18x-10(3x+8)+16=0[/tex]
[tex]x^2+9x^2+48x+64-18x-30x-80+16=0[/tex]
[tex]10x^2=0[/tex]
Thus the coefficients:
[tex]\boxed{Discriminant\ (D)=b^2-4ac}[/tex]
[tex]D=0^2-4(10)(0)[/tex]
[tex]=0[/tex]
Since the Discriminant = 0, then proven that the Linear Line is tangent to the Circle.
