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Tangent to the ellipse (x^(2))/(32)+(y^...

Tangent to the ellipse ` (x^(2))/(32)+(y^(2))/(18)=1` having slope `-(3)/(4)` meet the coordinates axes in A and B. Find the area of the `DeltaAOB` , where O is the origin .

A

12 sq. unit

B

8 sq unit

C

24 sq unit

D

32 sq unit

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Verified by Experts

The correct Answer is:
C
Equation of tangent with slope ` -(3)/(4)` is
`y=-(3)/(4)x +c `
According to condiltion of tengency
` c=sqrt(3 xx ((-3)/(4))^(2)+18)`
`= sqrt(18+ 18)` =6
`:. y=-(3)/(4)x+6`
`implies 4y+3x=24`
It meets the coordinate axes in A and B .
`:. A-=(8,0) and B-=(0,6)`
Required area `=(1)/(2) xx 8 xx 6=24 sq`. unit
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