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  • The segments of the focal chord PSQ of a parabola are the roots of the equation <img alt="\mathrm{2 x^{2}-17 x+7=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%20x%5E%7B2%7D

The segments of the focal chord PSQ of a parabola are the roots of the equation \mathrm{2 x^{2}-17 x+7=0}.Then the distance between tangent at vertex and directrix of the parabola is

Option: 1

\frac{7}{17}


Option: 2

\frac{14}{17}


Option: 3

\frac{17}{7}


Option: 4

\frac{17}{14}


Answers (1)

best_answer

SP, SQ are the roots of the equation \mathrm{2 x^{2}-17 x+7=0}

 \mathrm{PSQ\, \text{is a focal chord}\Rightarrow \frac{1}{\mathrm{SP}}+\frac{1}{\mathrm{SQ}}=\frac{1}{\mathrm{a}}}

\mathrm{\frac{\mathrm{SP}+\mathrm{SQ}}{\mathrm{SP} . \mathrm{SQ}}=\frac{1}{\mathrm{a}} \Rightarrow \mathrm{a}=\frac{7}{17}}

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vinayak

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