SOLUTION: The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices.

Question 1055387: The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

.
.
.
.Plotting the graph of the ellipse and the function shows that if the four lines lie within the ellipse and does not intersect the ellipse. If , the lines also do not intersect the ellipse. For , the lines intersect the ellipse in 8 points. The only value where there are 4 points of intersection is
.
.
.
At that point, it's the sum of 4 triangle areas with a base of 4 and height of 2,

RELATED QUESTIONS
This maths homework is killing me. f(x)=-x^2+6x+16 a) Write f(x) in the form... (answered by stanbon)

find a b C and the center and sketch the graph of the ellipse 4x^2 + 25 y^2 +16 X - 150y... (answered by lwsshak3)

Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the... (answered by ewatrrr)

Find the intersection points of the ellipse and the hyperbola: 5x^2+y^2=16... (answered by Alan3354)

Consider the line x/4 + y/8 = k where k is a positive number. a) In terms of k, write... (answered by stanbon)

graph the ellipse x^2+4y^2=64 (answered by gonzo)

Determine whether or not each equation is that of an ellipse, if it is not, state the... (answered by ikleyn)

Find the equation of the graph which meets the x-axis at -4 and 2 and its coordinates of... (answered by Alan3354)

Write the equation in standard form. State whether the graph of the equation is a... (answered by lwsshak3)