question_answer

The equation to the locus of the middle point of the portion of the tangent to the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] included between the co-ordinate axes is the curve

A)  \[9{{x}^{2}}+16{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]         

B)  \[16{{x}^{2}}+9{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]

C)  \[3{{x}^{2}}+4{{y}^{2}}=4{{x}^{2}}{{y}^{2}}\]          

D)  \[9{{x}^{2}}+16{{y}^{2}}={{x}^{2}}{{y}^{2}}\]