If the tangent to the curve [y = x x^2 - 3] , [x ,( x 3 )], at a point ([ ], [ ]) [ ] (0, …

Question

If the tangent to the curve $$y = {x \over {{x^2} - 3}}$$
, $$x \in \rho ,\left( {x \ne  \pm \sqrt 3 } \right)$$, at a point ($$\alpha $$, $$\beta $$) $$ \ne $$ (0, 0) on it is parallel to the line
2x + 6y -- 11 = 0, then :

Accepted Answer

$${{dy} \over {dx}}{|_{(\alpha ,\beta )}} = {{ - {\alpha ^2} - 3} \over {{{\left( {{\alpha ^2} - 3} \right)}^2}}}$$

Given that $${{ - {\alpha ^2} - 3} \over {{{\left( {{\alpha ^2} - 3} \right)}^2}}} =  - {1 \over 3}$$

$$ \Rightarrow $$ $$\alpha $$ = 0, $$ \pm $$ 3 ($$\alpha \ne $$ 0)

Solutions · 1