6. Advanced Topics

Conic Sections — Quiz

Test your understanding of conic sections with 5 practice questions.

Practice Questions

Question 1

Convert the general conic equation 3x^2+12x+4y^2-16y+4=0 to its standard form and identify its center.

Question 2

Which condition on the discriminant $B^2-4AC$ of the general second-degree equation $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ indicates the graph is a parabola?

Question 3

Given the ellipse $\frac{(x-1)^2}{9}+\frac{(y+2)^2}{16}=1$, what are the equations of its directrices?

Question 4

Which of the following is the equation of the director circle of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$?

Question 5

Identify the conic defined parametrically by $x=4\cos t-1,\;y=2\sin t+3$ and give its Cartesian equation.