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Equation of Tangent line

The slope of the radius is the negative

reciprocal to the slope of the tangent line.

The circle above is defined by the equation x2

y2 100. A tangent line (4x 3y 50)

intersects the circle at a point of tangency

(8,6). The tangent line is perpendicular to the

radius of the circle.

The circle above is defined by the equation x2

y2 100. A tangent line (4x 3y 50)

intersects the circle at a point of tangency

(8,6). The tangent line is perpendicular to the

radius of the circle.

The circle above is defined by the equation x2

y2 100. A tangent line (4x 3y 50)

intersects the circle at a point of tangency

(8,6). The tangent line is perpendicular to the

radius of the circle.

The circle above is defined by the equation x2

y2 100. A tangent line (4x 3y 50)

intersects the circle at a point of tangency

(8,6). The tangent line is perpendicular to the

radius of the circle.

When a tangent and a radius intersect at the

point of tangency, they are always perpendicular

to each other. It then follows that their slopes

are always negative reciprocals of each other.

Find the slope of the line tangent to the circle

x2 y2 5 and passing through the point R(-2,1).

Find the equation of the tangent to the circle x2

y2 10x 24y 0 and passing through the

point T(0,0).

(x2 10x 25) (y2 24y 144) 0 25 144

(x 5)2 (y 12)2 169

Centre (-5,12) r 13

12(y 0) 5(x 0)

12y 5x

5x 12y 0

Find the equation of the tangent to the circle x2

y2 6y - 16 0 and passing through the point

T(3,7).

Step 1 Find the centre and the radius.

x2 y2 6y - 16 0

x2 (y2 6y 9) 16 9

x2 (y 3)2 25

Centre (0,3) r 5

4(y 7) -3(x 3)

4y - 28 -3x 9

3x 4y 9 28

3x 4y 37

finito

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