Question

Write and equation of the translated or rotated graph in general form (picture below)

Answer 1

Answer:

Option b

Step-by-step explanation:

The equation $4x ^ 2 + 5y ^ 2 = 20$ has center in (0,0).

But the transformation $T(5, -6)$ shifts the center of the equation to the point (5, -6).

Therefore, when applying $T(5, -6)$ we will have the following equation translated.

$4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20$.

Simplifying we have:

$4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20$

Now we expand $(x-5) ^ 2$ and $(y + 6) ^ 2$

$4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0$

The equation of a circle has the form

$h(x-a) ^ 2 + q(y-b) ^ 2 = r$

For h = 1 and q = 1.

If $h \neq 1$ and $q\neq 1$ then the graph becomes an ellipse.

In this problem h = 4 and q = 5 therefore the figure is an ellipse