if-p-and-q-are-lengrhs-of-the-line-segment-of-any-focal-chord-of-parabola-y-2-4ax-where-p-q-are-the-roots-of-the-equation-5-2-x-2-4-5-x-4-5-0-then-the-length-of-the-semi-letusrectum

Question Number 48919 by vajpaithegrate@gmail.com last updated on 30/Nov/18

$$\mathrm{if}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{lengrhs}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segment} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{focal}\:\mathrm{chord}\:\mathrm{of}\:\mathrm{parabola}\:\mathrm{y}^{\mathrm{2}} =\mathrm{4ax}. \\ $$$$\mathrm{where}\:\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{5}+^{} \sqrt{}\mathrm{2}\:\right)\mathrm{x}^{\mathrm{2}} −\left(\mathrm{4}+\sqrt{\mathrm{5}}\right)\mathrm{x}+\left(\mathrm{4}+\sqrt{}\mathrm{5}\right)=\mathrm{0}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{semi}\:\mathrm{letusrectum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{is} \\ $$$$\mathrm{ans}:\mathrm{2} \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Nov/18

$${b}^{\mathrm{2}} −\mathrm{4}{ac} \\ $$$$\left(\mathrm{4}+\sqrt{\mathrm{5}}\:\right)^{\mathrm{2}} −\mathrm{4}\left(\mathrm{5}+\sqrt{\mathrm{2}}\:\right)\left(\mathrm{4}+\sqrt{\mathrm{5}}\:\right) \\ $$$$\left(\mathrm{4}+\sqrt{\mathrm{5}}\:\right)\left(\mathrm{4}+\sqrt{\mathrm{5}}\:−\mathrm{20}−\mathrm{4}\sqrt{\mathrm{2}}\:\right) \\ $$$$\left(\mathrm{4}+\sqrt{\mathrm{5}}\:\right)\left(−\mathrm{16}+\sqrt{\mathrm{5}}\:−\mathrm{4}\sqrt{\mathrm{2}}\:\right)<\mathrm{0} \\ $$$${so}\:{roots}\:{are}\:{not}\:{real}…{check}\:{question}.. \\ $$$${purchase}\:{good}\:{book}\:{from}\:{market}… \\ $$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com