Question 1055387
*[illustration lp11.JPG].
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.Plotting the graph of the ellipse and the function shows that if {{{c<2}}} the four lines lie within the ellipse and does not intersect the ellipse. If {{{c>5.66}}}, the lines also do not intersect the ellipse. For {{{4<c<5.66}}}, the lines intersect the ellipse in 8 points. The only value where there are 4 points of intersection is {{{c=4}}}
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At that point, it's the sum of 4 triangle areas with a base of 4 and height of 2,
{{{A=4*(1/2)(4)(2)}}}
{{{A=16)}}}