# Ellipse intersect circle

1. Sep 16, 2010

### femas

Hi

Let's say that we have equation of circle as

x2 + y2 = R2

and equation of ellipse in quadratic form as

A x2 + B y2 + Cx + D = 0

if the circle is inside the ellipse, so there is no intersection ...
Are x and y imag in this case? /or/ is one of them imag and the other is real ?... etc.

2. Sep 16, 2010

### rock.freak667

No intersection would lead to say 'x' being a complex number.

So if you sub x=a+bi into any of the equations you will see that x2 gives a complex number as well, which would lead to 'y' being complex as well.

3. Sep 16, 2010

### femas

But 'x' may be real but greater than R which makes 'y' to be pure imaginary.

So I don't know what is the case that makes 'x' real?

4. Sep 16, 2010

### rock.freak667

Well if you are plotting on the cartesian plane, then I don't think you would see a geometric reason, if you perhaps plot it on an Argand diagram, you might see a geometric reason.

5. Sep 16, 2010

### D H

Staff Emeritus
Sure it would. Let's look at

\aligned \phantom1 x^2+\phantom1 y^2 &= \phantom1 1 \\ 9x^2 + 4y^2 &= 36 \endaligned

The solutions (there are four of them) are given by $x^2=32/5$, $y^2=-27/5$. Note that in this case y is pure imaginary.