Q.

Let ' O ' be origin and the curve y=|x+9| meets the x-axis and y-axis respectively at A and B. Which of the following is / are correct

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a

The abscissa of the point where the tangent at B intersect the curve again is −36+182

b

Normal at  A to the curve is x+9=0

c

Tangent at B meets the tangent at A at (α,β) such that α+β=−152

d

The area of quadrilateral formed by the tangents at A and B and the co-ordinate  axes is 334 square units

answer is A.

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Detailed Solution

A=-9,0, and B=0,3 Tgt at Bx−6y+18=0 Solving with y2=−x−9⇒y2=−(6y−18)−9⇒y2+6y−9=0⇒y=−3+32⇒x=−36+182 Solving x−6y+18=0 and x+9=0⇒−9,32⇒α+β=−152 Area =12−93293=12−27−272=814
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Let ' O ' be origin and the curve y=|x+9| meets the x-axis and y-axis respectively at A and B. Which of the following is / are correct