Asked by Valerie

An ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3)$ and $(2, -8).$ Find the length of the major axis.
Answered by Asra
Hey bot
Answered by oobleck
The major axis clearly lies on the line x = 2, with the center at (2,-11/2).
So a = 11/2 and the major axis has length 11.
Answered by Asra
Find me a refrigerator that's 28 cubic feet, has a water dispenser and a French door, for under 2000$
Answered by Asra
Find me a leather, accent chair, for 200$
Answered by Bot
Hello! How can I assist you today?
Answered by Bot
That's correct! Since the ellipse is tangent to both the $x$-axis and the $y$-axis, its center lies on the line $x=2$ and $y=-\frac{11}{2}.$ Therefore, the distance from the center to each focus is $c=\frac{5}{2}.$ The length of the major axis is $2a,$ where $a$ is the distance from the center to each vertex. Using the Pythagorean theorem, we have:

$$a^2+c^2= (\frac{11}{2})^2 + (\frac{5}{2})^2 = \frac{125}{4}$$

Since $a$ is positive, we take the positive square root to get $a=\frac{\sqrt{125}}{2}=\frac{5\sqrt{5}}{2}.$ Thus, the length of the major axis is $2a=2\cdot\frac{5\sqrt{5}}{2}=5\sqrt{5}.$
Answered by Bot
One refrigerator that matches your criteria is the LG LFXS28968S. It has a capacity of 28 cubic feet, a water dispenser, and French doors. It is priced at around $1,900 on various online retailers such as Best Buy, Home Depot, and Amazon. Note that prices may vary based on location and availability.
Answered by Bot
Certainly! Here is a leather accent chair that is priced around $200:

1. Rivet Andrews Contemporary Top-Grain Leather Accent Chair - This chair features a sleek and modern design with genuine top-grain leather upholstery. It has a comfortable cushioned seat and sturdy wooden legs. The price for this chair is approximately $200 and can be found on Amazon.

Please note that prices may vary depending on the retailer and any ongoing discounts or promotions. Additionally, availability may vary as well.