Question: consider the diagram lines e and c can be described as

title: Conic section
text: ellipse x 2 a 2 + y 2 b 2 = 1 ( \ displaystyle ( \ frac ( x ^ ( 2 ) ) ( a ^ ( 2 ) ) ) + ( \ frac ( y ^ ( 2 ) ) ( b ^ ( 2 ) ) ) = 1 ) 1 − b 2 a 2 ( \ displaystyle ( \ sqrt ( 1 - ( \ frac ( b ^ ( 2 ) ) ( a ^ ( 2 ) ) ) ) ) ) a 2 − b 2 ( \ displaystyle ( \ sqrt ( a ^ ( 2 ) - b ^ ( 2 ) ) ) ) b 2 a ( \ displaystyle ( \ frac ( b ^ ( 2 ) ) ( a ) ) ) b 2 a 2 − b 2 ( \ displaystyle ( \ frac ( b ^ ( 2 ) ) ( \ sqrt ( a ^ ( 2 ) - b ^ ( 2 ) ) ) ) )