If Mxo,yo is the point on the curve $$3x2$$−$$4y2=72$$ which is nearest to the line $$3x+2y+1=0$$, then the value of $$xo+yo$$ is equal to

Question

If Mxo,yo is the point on the curve $$3x2$$−$$4y2=72$$ which is nearest to the line $$3x+2y+1=0$$, then the value of $$xo+yo$$ is equal to

Infinity Learn · Accepted Answer

Slope of the give line $$=$$−$$32$$ The points on the curve at which the tangent is parallel to the given line. So,  differentiating both sides with respect to x of $$3x2$$−$$4y2=72$$ we get $$dydx=3x4y=$$−$$32($$ given $$)$$⇒$$xy=$$−$$2$$ Now $$3xy2$$−$$4=72y2$$⇒$$y2=9$$⇒$$y=$$−$$3$$,$$3$$ So, points are $$($$−$$6$$,$$3)$$ and (6$$,−$$3) Now, distance of $$($$−$$6$$,$$3)$$ from the given line $$=$$−$$18+6+113=1113$$ And distance of (6$$,−$$3) from the given line $$=18$$−$$6+113=1313$$ Clearly, the required point is on $$($$−$$6$$,$$3)=x0$$,yo (given)  So, $$xo=$$−$$6$$,$$yo=3$$ Hence $$x0+y0=$$−$$6+3=$$−$$3$$

$If M (x_{o}, y_{o}) is the point on the curve 3 x^{2} - 4 y^{2} = 72 which is nearest to the line$
$3 x + 2 y + 1 = 0, then the value of (x_{o} + y_{o}) is equal to$

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If Mxo,yo is the point on the curve 3x2−4y2=72 which is nearest to the line 3x+2y+1=0, then the value of xo+yo is equal to

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$If M (x_{o}, y_{o}) is the point on the curve 3 x^{2} - 4 y^{2} = 72 which is nearest to the line$
$3 x + 2 y + 1 = 0, then the value of (x_{o} + y_{o}) is equal to$