The product of slopes of conjugate diameters of ellipse

Find The product of slopes of conjugate diameters of ellipse in the following question

Solution :

Two Lines \[y=m_1 x,y=m_2 x\] will be conjugate diameters of the ellipse \[x^2/a^2 +y^2/b^2 =1\] if the product of their slopes is equal to
\[-b^2/a^2 \]That is
\[ m_1 m_2=-b^2/a^2 \]Correct option is (4).