Find the largest and smallest distances from the origin to the conic whose equation is 5x^2 - 6xy + 5y^2 - 32 = 0

a. What is the best way of determining whether the given equation is a circle? b. How will you describe the graphs of the equations that are not circles?

Let A be a symmetric ${\displaystyle 2\times 2}$ matrix and let k be a scalar. Prove that the graph of the quadratic equation ${\displaystyle x^T}$ Ax=k is ,an ellipse, circle, or imaginary conic if ${\displaystyle k\ne q0}$ and det A > 0

Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of $A{x}^2+B{y}^2=C$ can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.

Use your some other reference source to find real-life applications of (a) linear differential equations and (b) rotation of conic sections that are different than those discussed in this section.

To determine: Find the lateral area of the conical tent.

How can you distinguish parabolas from other conic sections by looking at their equations?

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r\cos (?),y=k+r\sin (?)$ Use your result to find a set of parametric equations for the line or conic section. $(When0\le ?\le 2?.)$ Circle: center: (6, 3), radius: 7