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Category: Coordinate Geometry

Question-205631

Question Number 205631 by Lindemann last updated on 26/Mar/24 Answered by A5T last updated on 26/Mar/24 $${If}\:{angle}\:{between}\:{x}\:{and}\:{x}+\mathrm{17}\:{is}\:\mathrm{90}° \\ $$$$\left({x}+\mathrm{18}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +\left({x}+\mathrm{17}\right)^{\mathrm{2}} \Rightarrow{x}=\mathrm{7} \\ $$$$\frac{\mathrm{7}×\mathrm{24}}{\mathrm{2}}={r}\left(\frac{\mathrm{7}+\mathrm{24}+\mathrm{25}}{\mathrm{2}}\right)\Rightarrow{r}=\mathrm{3} \\…

We-define-a-domino-as-being-and-ordered-pair-of-distinct-integers-A-suitable-sequence-of-dominos-is-a-list-of-distinct-dominoes-in-which-the-first-coordonate-of-each-pair-after-the-first-is-equal-to-

Question Number 205654 by Lindemann last updated on 26/Mar/24 $${We}\:{define}\:{a}\:{domino}\:{as}\:{being}\:{and}\:{ordered}\:{pair}\:{of}\:{distinct} \\ $$$${integers}.\:{A}\:{suitable}\:{sequence}\:{of}\:{dominos}\:{is}\:{a}\:{list}\:{of}\:{distinct} \\ $$$${dominoes}\:{in}\:{which}\:{the}\:{first}\:{coordonate}\:{of}\:{each}\:{pair}\:{after} \\ $$$${the}\:{first}\:{is}\:{equal}\:{to}\:{the}\:{second}\:{coordonate}\:{of}\:{the}\:{immediately} \\ $$$${preceding}\:{pair},\:{and}\:{in}\:{which}\:{the}\:{pairs}\:\left({i};{j}\right)\:{and}\:\left({j};{i}\right) \\ $$$${do}\:{not}\:{both}\:{appear}\:{for}\:{all}\:{i}\:{and}\:{j}.\:{Let}\:{D}_{\mathrm{40}} \:{the} \\ $$$${set}\:{of}\:{all}\:{dominoes}\:{whose}\:{coordonate}\:{are}\:{not}\:{greater} \\ $$$${than}\:\mathrm{40}.\:{Find}\:{the}\:{length}\:{of}\:{the}\:{longest}\:{suitable}\:{sequence}…

Question-205517

Question Number 205517 by BaliramKumar last updated on 23/Mar/24 Answered by mr W last updated on 23/Mar/24 $${AB}=\sqrt{\left(\mathrm{5}−\mathrm{4}\right)^{\mathrm{2}} +\left(\mathrm{7}−\mathrm{3}\right)^{\mathrm{2}} }=\sqrt{\mathrm{17}} \\ $$$${say}\:{D}\:{divides}\:{AB}\:{externally}\:{and} \\ $$$${C}\:{divides}\:{AB}\:{internally}. \\…

I-A-5-1-B-3-5-C-5-2-ar-ABC-II-A-5-3-B-2-5-C-5-3-D-4-3-ar-ABCD-shortest-solution-

Question Number 204062 by BaliramKumar last updated on 05/Feb/24 $$\mathrm{I}.\:\:\:\:\:\:\:\mathrm{A}\left(−\mathrm{5},\:−\mathrm{1}\right);\:\mathrm{B}\left(\mathrm{3},\:−\mathrm{5}\right);\:\mathrm{C}\left(\mathrm{5},\:\mathrm{2}\right)\:\:\:\:\:\:{ar}\left(\bigtriangleup\mathrm{ABC}\right)\:=\:? \\ $$$$\mathrm{II}.\:\:\:\:\:\mathrm{A}\left(\mathrm{5},\:\mathrm{3}\right);\:\mathrm{B}\left(\mathrm{2},\:\mathrm{5}\right);\:\mathrm{C}\left(−\mathrm{5},\:\mathrm{3}\right);\:\mathrm{D}\left(−\mathrm{4},\:−\mathrm{3}\right)\:\:\:\:\:\:\:{ar}\left(\Box\mathrm{ABCD}\right)\:=\:? \\ $$$$\mathrm{shortest}\:\mathrm{solution}\: \\ $$ Answered by mr W last updated on 05/Feb/24 $${I}.…

Focus-and-vertex-of-a-parabola-are-at-3-4-and-0-0-Find-the-equation-of-the-directrix-

Question Number 203465 by princemurtuja last updated on 19/Jan/24 $$\mathrm{Focus}\:\mathrm{and}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{are}\:\mathrm{at}\:\left(\mathrm{3},\:\mathrm{4}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{0}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{directrix}. \\ $$ Answered by mr W last updated on 20/Jan/24 $${F}\left(\mathrm{3},\:\mathrm{4}\right) \\ $$$${V}\left(\mathrm{0},\:\mathrm{0}\right)…