Question

Classify the conic section without graphing: 3x^2 - 2xy + 3y^2 + 2x - 4y + 1=0

Answer 1

Circle: When x and y are both squared and the coefficients on them are the same — including the sign.

For example, take a look at 3x2 – 12x + 3y2 = 2. Notice that the x2 and y2 have the same coefficient (positive 3). That info is all you need to recognize that you’re working with a circle.

Parabola: When either x or y is squared — not both.

Answer 2

Hint: On conic, we must categorise the provided statement. As a result, we must compare the given phrase to the generic form of a conic. We receive the required response after conducting some classification.

Complete the following steps in order:

The fact is that the conic is$-3x^{2} -3y^{2} +6x+4y+1=0$

The conic must be classified.

A few principles must be followed in order to classify the conic. These are the following:

A conic's general shape is$Ax^{2} +Bx^{2} +Dx+Ey+F=0$

If A = B, the conic is a line; if A or B = 0, the conic is a circle; if A or B = 0, the conic is a parabola.

If A does not equal B and AB is greater than zero, the conic is an ellipse; if AB is less than zero, the conic is a hyperbola.

The offered conic fulfils the first of our requirements. A=B=−3

So, this conic is a circle.