Respuesta :
According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:
y = -x + 6.
What is the equation of the circle?
The equation of a circle of center [tex](x_0,y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem, we have that the center is at point (0,2), hence:
[tex]x^2 + (y - 2)^2 = r^2[/tex]
It goes through point (3,3), hence:
[tex]3^2 + (3 - 2)^2 = r^2[/tex]
[tex]r^2 = 10[/tex]
Hence, the equation is:
[tex]x^2 + (y - 2)^2 = 10[/tex]
What is the equation of the tangent line at point W?
It is given by:
[tex]y - y(0) = \frac{dy}{dx}|_{W}(x - x(0))[/tex]
Applying implicit differentiation, we have that:
[tex]2x + 2y\frac{dy}{dy} = 0[/tex]
[tex]\frac{dy}{dx} = -\frac{x}{y}[/tex]
Point W(3,3), hence:
[tex](x_0, y_0) = (3,3)[/tex]
[tex]\frac{dy}{dx} = -\frac{3}{3} = -1[/tex]
Hence the equation is:
y - 3 = -(x - 3).
y = -x + 6.
More can be learned about the equation of a tangent line at https://brainly.com/question/8174665
