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If`M(x_o,y_o)` is the point on the curve `3x^2-4y^2=72` which is nearest to the line `3x+2y+1=0`, then the value of `(x_o + y_o)` is equal to (A) 3 (B) `-3` (C) 9 (D) `-9` |
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Answer» `3x^2-4y^2=72` `m=-3/2` `6x-8y(dy)/(dx)=0` `(dy)/(dx)=(3x)/(4y)` `(3x_0)/(4y_0)=-3/2` `x_o=-2y_o` `8y_o^2=72` `y=pm3` `3x+2y+1=0` `3x+2y+c=0` `c=-3x_0-2y_o` `|c-1| is minimum=4y_0` |c-1| is minimum at` c=12 andy_o=3` `x_0+y_0=3+3*(-2)=-3` option b is correct. |
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