InterviewSolution
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InterviewSolution
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Let `vec(r)` is a positive vector of a variable pont in cartesian OXY plane such that `vecr.(10hatj-8hati-vecr)=40` and `p_1=max{|vecr+2hati-3hatj|^2},p_2=min{|vecr+2hati-3hatj|^2}`. A tangent line is drawn to the curve `y=8/x^2` at the point A with abscissa 2. The drawn line cuts x-axis at a point BA. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - c Let `vecx= x hati + yhatj` `x^(2) + y^(2) + 8x - 10y + 40 =0` , which is a circle centre C(-4,5) , radius r = 1 `p_(1)= max {(x+2)^(2)+ (y-3)^(2)}` `P_(2) = min {(x+2)^(2)+ (y-3)^(2)}` Let P be (-2,3). Then `CP = sqrt2,r=1` ` P_(2)= (2sqrt2-1)^(2)` `P_(1) = (2sqrt2+1)^(2)` `P_(1) + p_(2) =18` Slope = AB = `((dy)/(dx))_(2,2)=-2` Equation of AB, 2x+y=6 `vec(OA)=2hati=2hatj,vec(OB)= 3hati` `vec(AB)=hati-2hatj` `vec(AB).vec(OB)= (hati-2hatj) (3hati)=3` |
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