# Circle equation help

1. May 14, 2005

### roger

hi, I am stuck on this question for homework :

I'm not sure how to find the answer, as I thought integration is used only if the curve intersects at the x axis ?

Thanx for any help

1.) The equation of circle x^-8x+y^2-10y=-16

It intersects the y axis at two points : (0,2) and (0,8)

Find the small area between the curve and the y axis.(on the left of the y axis)

2.) Also, the chord between 0,2 and 0,8 on the circle subtends an angle at the centre (4,5).

Show that the angle is 7/25 using the cosine rule.

I'm not sure what to do here as well..

2. May 14, 2005

### dextercioby

Plot that circle and then decide whether u'll be needing calculus to find that area.

As for the second,i don't follow.Is it the same circle...?

Daniel.

3. May 14, 2005

### roger

The area is bound between the y axis and the circle. But I don't see how else it could be done without calculus ?

The second question is the same circle and I need to find the angle .
(0,2) and (0,8) is the chord on the circle .

4. May 14, 2005

### dextercioby

Alright,then,write the equation and see which branch of the explicitation will u be needing (hint:u can explicitate "x" as a function of "y",because you're given the intercepts with the Oy axis).

Daniel.

5. May 14, 2005

### roger

I've not heard that word before...explicitate ..

but I dont understand what your saying.

6. May 14, 2005

### dextercioby

$$(x-x_{0})^{2}+(y-y_{0})^{2}=1$$

Express x=x(y).

Daniel.

7. May 14, 2005

### roger

I dont get it :grumpy:

especially
Express x=x(y).

8. May 14, 2005

### dextercioby

You need to put somethting,a function,in this integral

$$\mbox{Area}=\int_{\mbox{intercept no.1}}^{\mbox{intercept no.2}} f(y) \ dy$$

And that function of "y" (f(y)) is the one u'll be getting from the circle's equation.

Daniel.

9. May 14, 2005

### roger

okay, and then take away the the intercept 2 - 1 ?

but what does x(y)=x mean ? I need a thorough explanation on this please.

10. May 14, 2005

### dextercioby

It's a notation;x=x(y) means the function "x" written in terms of the variable "y".

Daniel.

11. May 14, 2005

### roger

but if i took away the 1st from the second integral is the order important ?

what difference does it make ?

If the area was not bound by either x or y axis is there a direct way to calulate the area?

12. May 14, 2005

### dextercioby

Yes,of course.The area of a plane domain $D\subseteq\mathbb{R}^{2}$ is given by

$$S_{D}=:\iint_{D} dx \ dy$$

as long as u choose Oxy as a set of orthormal coordinates in the plane.

Daniel.

13. May 15, 2005

### roger

Daniel, what difference would it make if I wrote g(y)=x ?

14. May 15, 2005

### arildno

The difference is that x=x(y) is a "loose/sloppy" notation, whereas x=g(y) is an example of a "rigorous/careful" notation. That's basically it.