Circles

Question 1

What is the equation of a circle?

Answer 1

(x-a)* + (y-b)= r
For example: (x-3)+(y-4)=25
x=3 y=4 r=5

Question 2

What’s a tangent?

Answer 2

A tangent is a line that intersects the circle in exactly one point.
The point of tangency is the point where a tangent line intersects the circle.

Question 3

What’s the equation of a tangent?

Answer 3

A tangent is a straigth line, therefore it’s equation is y=mx+c.
Example: The equation of a circle is x+y= 25, find the
equation of the tangent at point (4,-3).
Find the gradient of the line between the
points (0,0) and (4,-3). In this case the gradient
is -4/3, therefore the gradient of the tangent =
3/4. Then plot the gradient back in the
equation and find c.