# hi! conics

• Dec 6th 2006, 07:45 AM
bay
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? :confused:
• Dec 6th 2006, 07:56 AM
ThePerfectHacker
Quote:

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.
• Dec 6th 2006, 08:07 AM
Soroban
Hello, bay!

Evidently, you need help . . .

Quote:

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)