2x^2+Cy^2+Dx+Ey+F=0 represents a conic. state the values of C for which each of the following are possible
The general form of a second-degree quadratic in 2 variables is
We have to check the expression to determine the type of conic.
If , then we have a hyperbola.
If , then we have a parabola.
If , then we have either a circle or an ellipse. If B = 0 and A = C, then we have a circle. Otherwise, it's an ellipse.
Now try your problem. B = 0 and A = 2...
You're expected to know the general forms of the four conics.
The coefficients of and must be equal.represents a conic.
State the values of for which each of the following are possible:
(a) a circle
The coefficients of and are unequal, but have the same sign.(b) an ellipse
The equation has or , but not both.(c) a parabola
The coefficients of and must have opposite signs.(d) a hyperbola