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Category: Coordinate Geometry

if-the-points-C-1-2-divides-internally-the-line-segment-joining-the-points-A-2-5-and-B-x-y-in-the-ratio-3-4-find-the-value-of-x-2-y-2-

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Question Number 24181 by gopikrishnan005@gmail.com last updated on 14/Nov/17 $${if}\:{the}\:{points}\:{C}\left(−\mathrm{1},\mathrm{2}\right)\:{divides}\:{internally}\:{the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:{A}\left(\mathrm{2},\mathrm{5}\right)\:{and}\:{B}\left({x},{y}\right)\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4}\:{find}\:{the}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Answered by mrW1 last updated on 14/Nov/17 $$\frac{−\mathrm{1}−\mathrm{2}}{{x}−\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{3}+\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{7}} \\ $$$$\Rightarrow\mathrm{3}\left({x}−\mathrm{2}\right)=\mathrm{7}\left(−\mathrm{1}−\mathrm{2}\right) \\ $$$$\Rightarrow{x}=−\mathrm{5}…

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the-line-segment-joining-the-points-3-4-and-1-2-is-trisected-at-the-points-P-and-Q-if-the-coordinates-of-P-and-Q-are-p-2-and-5-3-q-respectively-find-the-values-of-p-and-q-

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Question Number 24179 by gopikrishnan005@gmail.com last updated on 14/Nov/17 $${the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:\left(\mathrm{3},−\mathrm{4}\right)\:{and}\:\left(\mathrm{1},\mathrm{2}\right)\:{is}\:{trisected}\:{at}\:{the}\:{points}\:{P}\:{and}\:{Q}\:{if}\:{the}\:{coordinates}\:{of}\:{P}\:{and}\:{Q}\:{are}\:\left({p},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5}/\mathrm{3},{q}\right)\:{respectively}\:{find}\:{the}\:{values}\:{of}\:{p}\:{and}\:{q}. \\ $$ Answered by mrW1 last updated on 14/Nov/17 $$\frac{{x}_{\mathrm{1}} −\mathrm{3}}{\mathrm{1}−\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{x}_{\mathrm{1}} =\mathrm{3}−\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{7}}{\mathrm{3}} \\…

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The-distance-between-point-P-lat-65-S-long-25-E-and-Q-lat-65-S-long-X-on-the-earth-surface-along-the-parallel-of-latitute-is-2502-5-km-If-pi-22-2-and-earth-radius-is-6370-km-find-the-t

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Question Number 24100 by tawa tawa last updated on 12/Nov/17 $$\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{point}\:\:\mathrm{P}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\:\mathrm{long}\:\mathrm{25}°\mathrm{E}\right)\:\mathrm{and}\:\mathrm{Q}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\mathrm{long}\:\mathrm{X}\right) \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{surface}\:\mathrm{along}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitute}\:\mathrm{is}\:\:\mathrm{2502}.\mathrm{5}\:\mathrm{km}.\:\mathrm{If}\:\:\pi\:=\:\frac{\mathrm{22}}{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{earth}\:\mathrm{radius}\:\mathrm{is}\:\:\mathrm{6370}\:\mathrm{km},\:\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}. \\ $$ Commented by tawa tawa last updated on 12/Nov/17…

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Find-a-vector-function-F-whose-graph-is-the-the-line-of-intersection-of-the-plane-4x-2y-z-3-and-x-y-3y-1-

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Question Number 23870 by lizan 123 last updated on 08/Nov/17 $${Find}\:{a}\:{vector}\:{function}\:{F}\:\:{whose}\:{graph}\:{is}\:{the} \\ $$$${the}\:{line}\:{of}\:{intersection}\:{of}\:{the}\:{plane}\: \\ $$$$\mathrm{4}{x}−\mathrm{2}{y}+{z}=\mathrm{3}\:{and}\:{x}+{y}−\mathrm{3}{y}=\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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Question-89281

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Question Number 89281 by ajfour last updated on 16/Apr/20 Commented by ajfour last updated on 17/Apr/20 $${Both}\:{parabolas}\:{have}\:{same}\:{shape}. \\ $$$${If}\:{equation}\:{of}\:{one}\:{is}\:{y}={x}^{\mathrm{2}} , \\ $$$${and}\:{the}\:{inscribed}\:{triangle}\:{is} \\ $$$${eqiuilateral},\:{find}\:{the}\:{eq}.\:{of}\:{the} \\…

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