5. Let R be a rectangle inscribed into the ellipse x² y² 62 where a, b>0 a² + R = 1 A + = 1 (a) Suppose the x-coordinate of A is increasing at a constant rate 1 unit/s. At b A = (272). 9/12 (i) how fast will the y-coordinate of A decrease?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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5. Let R be a rectangle inscribed into the ellipse
x² y²
a² 6²
+
where a, b > 0
R
1
A
2.2
a²
+
6²
= 1
(a) Suppose the x-coordinate of A is increasing at a constant rate 1 unit/s. At
a
b
4- (272)
A =
9/12
(i) how fast will the y-coordinate of A decrease?
Transcribed Image Text:5. Let R be a rectangle inscribed into the ellipse x² y² a² 6² + where a, b > 0 R 1 A 2.2 a² + 6² = 1 (a) Suppose the x-coordinate of A is increasing at a constant rate 1 unit/s. At a b 4- (272) A = 9/12 (i) how fast will the y-coordinate of A decrease?
(a) Suppose the x-coordinate of A is increasing at a constant rate 1 unit/s. At
a
b
A =
(272).
/2 √2
(i) how fast will the y-coordinate of A decrease?
(ii) how fast will the area of R change?
(b) Find the coordinates of A when the area of R is maximized.
Transcribed Image Text:(a) Suppose the x-coordinate of A is increasing at a constant rate 1 unit/s. At a b A = (272). /2 √2 (i) how fast will the y-coordinate of A decrease? (ii) how fast will the area of R change? (b) Find the coordinates of A when the area of R is maximized.
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