Question

1. choose the best answer. which is the equation of an ellipse?

\\(\frac{(x - 5)^2}{16} + \frac{(y + 2)^2}{9} = 1\\)
\\(\frac{(x - 5)^2}{16} + \frac{(y + 2)^2}{9} = 1\\)
\\(\frac{(x - 5)^2}{16} - \frac{(y + 2)^2}{9} = 1\\)
\\((x - 5)^2 + (y + 2)^2 = 25\\)

Explanation:

For Question (11):

Step1: Multiply scalar by matrix

Multiply each element of the matrix by $-2$:

$$-2 \times
LATEXBLOCK1
=
LATEXBLOCK2
$$

Step2: Calculate each element

Compute the product for each entry:

$$\begin{bmatrix} -2 & -4 \\ -6 & 2 \\ -10 & 0 \end{bmatrix}$$

The standard equation of an ellipse with center $(h,k)$ is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ (where $a,b>0$, no subtraction terms, and it equals 1, not a constant like 25 which is a circle's form).

Answer:

$$\begin{bmatrix} -2 & -4 \\ -6 & 2 \\ -10 & 0 \end{bmatrix}$$

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For Question (12):