Equation of Tangent line

1
Equation of Tangent line
2
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.
3
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.
4
Find the slope of the line tangent to the circle
x2 y2 5 and passing through the point R(-2,1).
5
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
6
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
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