If the equation on reflection of $\frac{(x-4)^2}{16} + \frac{(y-3)^2}{9} = 1$ about the line $x - y - 2 = 0$ is $16x^2 + 9y^2 + k_1x - 36y + k_2 = 0$ then $\frac{k_1 + k_2}{100}$ is ______.
Step-by-Step Solution
Key Concept: Reflecting a conic about a line requires using the reflection formula and transforming the equation accordingly.
The image of point $(h,k)$ on the ellipse about the line $x - y - 2 = 0$ is $(k', h')$ where $\frac{h'-h}{1} = \frac{k'-k}{-1} = -2 = \frac{h-k-2}{1+1}$. This gives $h' = k+2, k' = h-2$. The reflection ellipse equation becomes $16x^2 + 9y^2 - 160x - 36y + 292 = 0$. Summing coefficients: $\frac{k_1 + k_2}{100} = \frac{292-160}{100} = 1.32$.
Correct Answer: 1.32