Use differentiation method to find the slope of the tangent hence the
equation of the tangent as shown below.
circle with radius = 5
and centre at (-3,1)
tagent of the
circle at x = -6

The equation of the tangent at x=-6 is

Step-by-step explanation:

The equation of a circle with center (h,k) with radius r units is given by:

The given circle has center (-3,1) and radius 5 units.

We substitute the center and the radius into the equation to get;

To find the slope, we differentiate implicitly to get:

When x=-6;we have

or  

From the graph the reuired point is (-6,-3).

We substitute this point to find the slope;

The equation is given by .

We plug in the slope and the point to get:

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