About a circle...?

Question

is the gradient of any tangen of the circle the same?
is it the same for every circle? or does it differ with the size of the circle? can anyone show me how to obtain the gradient?

Answer 1

Using the equation for the circle, you can find:
the centre point (call it (x0,y0)), the length of the radius and any point on the circumference.

As a rule, the tangent to a circle is perpendicular to the radius line at that point.

So, find the slope from the point (x,y) to the centre (x0,y0). The slope of the tangent will be the inverse of that slope.

Of course, if y = y0, your tangent's gradient will be infinite (or undefined).

Answer 2

The equation of a circle is x^2 +y^2 = r^2 where r is radius.
The gradient (or slope) of a tangent to a circle at any point (x,y) is simply -y/x. So its is different for each point on the circle. Also you can see that that the gradient does not depend on r: it depends only on x and y. Thus the circle can be any size.

If your circle was given by x^2 + y^2 = 25Then the gradient at the point (3,4) would be -y/x = -4//3.

Answer 3

You can have a tangent of any point of a circle. So no, it is not always the same gradient, nor does it depend on the size of the circle.

Answer 4

1. get the equation for the circle

2. find dx (x derivative)

3. find dy (y derivative)

4. find M --> M= dy/dx

5. M is the gradient

The gradient should be the same for any one circle. It should differ for the size of the circle as the equation for the circle changes. Good luck.