SOLUTION: Consider the ellipse x^2/9 + y^2/4 = 1 in the first quadrant.
Lines passing through the point (3/2, 1/4), which is inside this quarter-ellipse,
are free to pivot around it insi
Algebra.Com
Question 1183646: Consider the ellipse x^2/9 + y^2/4 = 1 in the first quadrant.
Lines passing through the point (3/2, 1/4), which is inside this quarter-ellipse,
are free to pivot around it inside this region up to the y- and x-intercepts (0,2) and (3,0), respectively.
What is the maximum or minimum area of the region that can be enclosed by the ellipse x^2/9 + y^2/4 = 1,
any of the pivoting lines around the point (3/2, 1/4), and the x or y axis?
Thank you in advance.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
The desired area in each case illustrated below is the area of the quarter ellipse minus the area of the shaded triangle. So, the larger the triangle, the smaller the desired area, and the minimum triangle gives the maximum desired area and vice versa. The area of the quarter ellipse without any subtractions is:
You can use a simple trig substitution to solve this integral. Hint: Take out the constant term and then let )
and du)
Then subtract the triangle areas illustrated:
John
My calculator said it, I believe it, that settles it
From
I > Ø
RELATED QUESTIONS
The line x/3 + y/4 = 1 forms a triangle with the x and y axes in the first quadrant.... (answered by greenestamps,robertb)
Consider the ellipse 49 x^2 + 1 y^2 = 4. (answered by tommyt3rd)
Find the eccentric angle in the first quadrant of a point on the ellipse {{{ x^2/10 +... (answered by MathLover1)
Consider the quarter-ellipse x^2/9 + y^2/4 = 1 at the 1st quadrant. Two points (0,1/2)... (answered by Alan3354,robertb,ikleyn)
My question is
Consider the line 2x-4y=5. Write the slope intercept equation of the... (answered by scott8148)
Solve all parts of following question:
1- Find the equation of the straight line... (answered by ikleyn)
What is the focal point of the ellipse (x+3)^2/16 + (y-1)^2/4... (answered by lwsshak3)
Write equations for the vertical and the horizontal lines passing through the point... (answered by jim_thompson5910)
'Lines in 3-Space' lesson:
1. State where possible vector, parametric, and symmetric... (answered by ikleyn)