YU says: Translate the parabola and the ellipse to make the y-axis the axis of symmetry. y=-8(x^2 - 1/4) and (x^2/a^2)+((y-b)^2)/(b^2)=1 to obtain 8a^2y^2 - (16a^2b+b^2)y + 2b^2 =0, a quadratic equation in y. Let Δ=0 to obtain b=8a-16a^2. Area of ellipse A = πab = π(8a^2 - 16a^3). A_max = 8π/27.
YU says:
ReplyDeleteTranslate the parabola and the ellipse to make the y-axis the axis of symmetry.
y=-8(x^2 - 1/4) and (x^2/a^2)+((y-b)^2)/(b^2)=1 to obtain
8a^2y^2 - (16a^2b+b^2)y + 2b^2 =0, a quadratic equation in y.
Let Δ=0 to obtain b=8a-16a^2.
Area of ellipse A = πab = π(8a^2 - 16a^3).
A_max = 8π/27.