Assertion $(A)$: The image of $\frac{x^2}{25}+\frac{y^2}{16}=1$ in the line $x+y=10$ is $\frac{(x-10)^2}{16}+\frac{(y-10)^2}{25}=1$.
Reason $(R)$: The image of a curve '$C$' in a line $L$ is the locus of the image of every point of $C$ with respect to the line $L$.
The correct option among the following is:

• A
  $(A)$ is true,$(R)$ is true and $(R)$ is the correct explanation for $(A)$
• B
  $(A)$ is true,$(R)$ is true but $(R)$ is not the correct explanation for $(A)$
• C
  $(A)$ is true but $(R)$ is false
• D
  $(A)$ is false but $(R)$ is true