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  • If is a tangent to the parabola <img alt="\mathrm{ y^2=4 a\left(x-\frac{1}{3}\ri

If \mathrm{y=2 x-3} is a tangent to the parabola \mathrm{ y^2=4 a\left(x-\frac{1}{3}\right) }, then \mathrm{' a^{\prime} } is equal to :

Option: 1

\frac{22}{3}


Option: 2

-1


Option: 3

\frac{14}{3}


Option: 4

-\frac{14}{3}


Answers (1)

best_answer

\mathrm{\text { Solving } y=2 x-3}                  \mathrm{\text { and } y^2=4 a\left(x-\frac{1}{3}\right)}

                                                        \mathrm{(2 x-3)^2=4 a\left(x-\frac{1}{3}\right)}

                                                      \mathrm{4 x^2+9-12 x=4 a x-\frac{4 a}{3}}

                             \mathrm{\mathrm{D}=0 ;\, \, \, \, \, \quad 16\left(3+\mathrm{a}^2\right)-16\left(9+\frac{4 \mathrm{a}}{3}\right)=0}

                                                      \mathrm{9+a^2+6 a=9+\frac{4 a}{3}}

                    \mathrm{a^2+\frac{4 a}{3}=0 \, \, \, \Rightarrow \, \, \, a=0 \text { or } a=\frac{14}{3}}

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avinash.dongre

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