If the chords of contact of tangents from two poinst `(x_1, y_1)` and `(x_2, y_2)` to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` are at right angles, then find the value of `(x_1x_2)/(y_1y_2)dot`

Options

A. `(a^(2))/(b^(2))`
B. `-(b^(2))/(a^(2))`
C. `-(a^(4))/(b^(4))`
D. `-(b^(4))/(a^(4))`

Answer

C

Explanation

the equation of the chords of contact of tangents drawn from `(x_(1),y_(1)) and ( x_(2),y_(2))` to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` are
`(x x_(1))/(a^(2))+(y y_(1))/(b^(2))=1`
`( x x_(2))/(a^(2))+( yy_(2))/(b^(2))=1`
it is given that (i) and (ii) are right angles.
`therefore (-b^(2))/(a^(2))(x_(1))/(y_(1))xx(-b^(2))/(a^(2))(x_(2))/(y_(2))=-1implies (x_(1)x_(2))/(y_(1)y_(2))=-(a^(4))/(b^(4))`