Question

Identify the equation without applying a rotation of axes.x squared +10xy+25y squared-2x-4y+10=0a. parabolab. ellipsec. hyperbolad. circle

Answer 1

We are given the equation

`x^2+10xy+25y^2-2x-4y+10=0`

We will first simplify the equation

`\begin{gathered} x^(2)+10xy+25y^(2)-2x-4y+10=0 \\ \left(x+5y\right)^2-2\left(x+y\right)+10=0 \\ (x+5y)^2=2(x+y)-10 \end{gathered}`

We draw the graph

From the graph, one can see that this is a rotated parabola

Correct answer is a Parabola

Option A