Step 1:

The circle equation is .

The line equations are , , and .

The line equations is in the form of , where is a positive integer.

Substitute in .

.

If the line is tangent to the graph of the circle then discriminant : .

Substitute and in .

.

Susbtitute in the line equation .

The tangent line equation to the curve is .

Solution :

The tangent line equation to the curve is .

The tangent line equation is

Discriminant

.

Discriment

.

Center of the circle is .

Radius of the circle is .Since a tangent only touches the circle at exactly one and only one point, that point must be perpendicular to a radius.

A line touches a circle if the distance of the center of the circle to the line is equal to the radius of the circle .

The perpendicular distance between circle equation   and a line is .

.

Consider tangent line equation(b) is .

.

.

Therefore, the tangent line equation of a circle is .

Solution:

The tangent line equation of the circle is .

Option (b) is correct.

Consider tangent line equation (c) is .

.

.

Consider tangent line equation(b) is .

.

.

Graph:

Graph the circle equation:.

Apply derivative on each side with respect to .

Apply power rule of derivatives: .

The standard form of circle equation is , where is center of the circle and is radius of circle.

Compare with standardform of circle equation.