Let A = ( , ) R R : | - 1| 4 and | - 5| 6 and B = ( , ) R R : 16( - 2)^2+ 9( - 6)^2 144 .

Question

Let A = { ($\alpha ,\beta $) $\in R	imes R$ : |$\alpha $ - 1| $\le 4$ and |$\beta $ - 5| $\le 6$ }

and B = { ($\alpha ,\beta $) $\in R	imes R$ : 16($\alpha $ - $2{)}^{2}$+ 9($\beta $ - $6{)}^{2}$ $\le 144$ }.

Then

Accepted Answer

$$\begin{aligned}
& \text { A: }|x-1| \leq 4 \text { and }|y-5| \leq 6 \
& \Rightarrow-4 \leq x-1 \leq 4 \Rightarrow-6 \leq y-5 \leq 6 \
& \Rightarrow-3 \leq x \leq 5 \quad \Rightarrow-1 \leq y \leq 11 \
& \text { B : } 16(x-2)^2+9(y-6)^2 \leq 144 \
& \text { B : } \frac{(x-2)^2}{9}+\frac{(y-6)^2}{16} \leq 1
\end{aligned}$$

From Diagram $\mathrm{B} \subset \mathrm{A}$

Solutions · 1