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A tangent having slope of -4/3 to the ...

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 `A` and `B ,` respectively. If `C` is the center of the ellipse, then find area of triangle `A B Cdot`

Text Solution

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The correct Answer is:
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.
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