1. Equation of Tangent line

2. is the negative reciprocal to the slope of the tangent line.
x2 + y2 = 100
circle
4x – 3y = 50
tangent line
(8,6)
point of tangency
The slope of the radius
is the negative reciprocal
to the slope of the
tangent line.
mr =
mt =
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.
T(0,-3)
P(2,-1)
C(-1,2)
P(2,-1)
mr =

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).
Step 1: Find the centre and the radius.
x2 + y2 + 10x – 24y = 0
(x2 + 10x + 25) + (y2 – 24y + 144) =
(x + 5)2 + (y – 12)2 = 169
Step 3: Find the slope of the tangent.
Centre: (-5,12) r = 13
Step 2: Find the slope of the radius.
Step 4: Find the equation of the tangent.
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) =
x2 + (y – 3)2 = 25
Centre: (0,3) r = 5
4(y – 7) = -3(x – 3)
4y - 28 = -3x + 9
3x + 4y =
3x + 4y = 37

7. finito