Question

A tangent having slope of `-4/3` to the ellipse `(x^2)/(18)+(y^2)/(32)=1` intersects the major and minor axes at points `Aa n dB ,` respectively. If `C` is the center of the ellipse, then find area of triangle `A B Cdot`

Answer 1

Correct Answer - 24 sq. units
For a given ellipse, the equation of tangent whsoe slope is m is `y=mx+sqrt(18m^(2)+32)`
For m=-4/3, the tangent is
`y=-(4)/(3)xxsqrt(18((16)/(9))+32)`
`=-(4)/(3)x+18`
or 4x+3y=24
This intersects the amjor and minor axes at (6,0) and B(0,8), respectively.