(a).

The circle equation is .

The tangent line equation .

Substitute in .

Compare with quadratic form .

.

The quadratic equation has only one solution.

Then discriminant .

.

(b).

Roots of the quadratic equation .

Since .

From part (a), .

Substitute the value of in .

The tangent point is .

(c).

Slope of the tangent line is .

 Slope of the line from the center to tangent point is .

Since the slopes are negative reciprocal to each other, they are perpendicular.

The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.

(a). .

(b). The tangent point is .

(c). The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.