Find the area of the largest rectangle that can be inscribed in the ellipse x^2/25 + y^2/16 = 1. Find the area of the largest rectangle that can be inscribed in the ellipse x225+y216=1. A. 35 C. 45 B. 40 D. 50 Solution Click here to… Jhun Vert Sat, 06/29/2024 - 15:13 Solution Click here to expand or collapse this section For largest rectangle x=a√2 and y=b√2 Amax=4xy Amax=4(5√2)(4√2) Amax=40 unit2 Detailed Solution Click here to expand or collapse this section x225+y216=1 y2=16(1−x225) y2=16(25−x225) y2=1625(25−x2) y=45√25−x2 Area of rectangle inscribed in the ellipse A=4xy A=4x(45√25−x2) A=165x√25−x2 For the largest rectangle dAdx=165[x⋅−2x2√25−x2+√25−x2⋅1]=0 x⋅−2x2√25−x2+√25−x2⋅1=0 −x2√25−x2+√25−x2=0 √25−x2=x2√25−x2 25−x2=x2 2x2=25 x=5√2 Area of the largest rectangle Amax=165⋅5√2⋅√25−252 Amax=40 unit2 Log in or register to post comments Log in or register to post comments
Solution Click here to… Jhun Vert Sat, 06/29/2024 - 15:13 Solution Click here to expand or collapse this section For largest rectangle x=a√2 and y=b√2 Amax=4xy Amax=4(5√2)(4√2) Amax=40 unit2 Detailed Solution Click here to expand or collapse this section x225+y216=1 y2=16(1−x225) y2=16(25−x225) y2=1625(25−x2) y=45√25−x2 Area of rectangle inscribed in the ellipse A=4xy A=4x(45√25−x2) A=165x√25−x2 For the largest rectangle dAdx=165[x⋅−2x2√25−x2+√25−x2⋅1]=0 x⋅−2x2√25−x2+√25−x2⋅1=0 −x2√25−x2+√25−x2=0 √25−x2=x2√25−x2 25−x2=x2 2x2=25 x=5√2 Area of the largest rectangle Amax=165⋅5√2⋅√25−252 Amax=40 unit2 Log in or register to post comments
Solution Click here to…