1. ## hi! conics

I am need of help!
the equation 2x^2+cy^2+dx+ey+f=0 represents a conic state the values of c for which each of the following are possible

a) circle
b) ellipse
c) parabola
d) hyperbola

so I am not sure but here is my guess:
a) circle: c=90
b) ellipse: c=50
c) parabola c=?
d) hyperbola c=?

I am not even sure?

2. Originally Posted by bay
I am need of help!
the equation 2x^2+cy^2+dx+ey+f=0 represents a conic state the values of c for which each of the following are possible

a) circle
b) ellipse
c) parabola
d) hyperbola
You need to look at the discrimanat.
The $\displaystyle xy$ term is zero here.
And the $\displaystyle x^2$ term is 2 and $\displaystyle y^2$ term is c.
Thus,
$\displaystyle -4(2)(c)^2=-8c^2$
Thus,
$\displaystyle -8c^2>0$ if $\displaystyle c\not = 0$ and we have an ellipse of a circle.
And only when $\displaystyle c=0$ we have $\displaystyle -8c^2=0$ thus we have parabola.

3. Hello, bay!

Evidently, you need help . . .

The equation $\displaystyle 2x^2+cy^2+dx+ey+f\:=\:0$ represents a conic.
State the values of $\displaystyle c$ for which each of the following are possible.

a) circle . . b) ellipse . . c) parabola . . d) hyperbola

a) Circle
The coefficients of $\displaystyle x^2$ and $\displaystyle y^2$ must be equal.
. . Hence: .$\displaystyle c = 2$

b) Ellipse
The coefficients of $\displaystyle x^2$ and $\displaystyle y^2$ must have the same sign but unequal.
. . Hence: .$\displaystyle c > 0,\;c \neq 2$ . (any positive number except 2)

c) Parabola
Either the coefficient of $\displaystyle x^2$ or the coefficient of $\displaystyle y^2$ must be zero.
. . Hence: .$\displaystyle c = 0$

d) Hyperbola
The coefficients of $\displaystyle x^2$ and $\displaystyle y^2$ must have oppsite signs.
. . Hence: .$\displaystyle c < 0$ . (any negative number)