A rectangle is inscribed in the ellipse {{MATH_1}} so that two of its edges are parallel to the {{MATH_2}}-axis, and the other two are parallel to the {{MATH_3}}-axis. Find the dimensions of the rectangle with the largest area. {{CMD_4}} {{CMD_5}} {{ENV_6}} {{CMD_7}} {{CMD_8}} {{CMD_9}} Area of the rectangle {{MATH_10}}. We will express {{MATH_11}} as a function of, say, {{MATH_12}}. Note that {{MATH_13}} and {{MATH_14}} satisfy the equation of the ellipse, so {{MATH_15}} Since in our figure {{MATH_16}}, we have {{MATH_17}} {{CMD_18}} {{CMD_19}} Now {{MATH_20}}.