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Category: Coordinate Geometry

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)…

shortest-distance-from-6-0-to-x-2-y-2-16-0-

Question Number 201829 by 281981 last updated on 13/Dec/23 $${shortest}\:{distance}\:{from}\:\left(−\mathrm{6},\mathrm{0}\right){to}\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\mathrm{16}=\mathrm{0} \\ $$ Answered by esmaeil last updated on 13/Dec/23 $${d}=\sqrt{\left({x}+\mathrm{6}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} }=\sqrt{\overset{\mathrm{2}} {{x}}+\mathrm{12}{x}+\mathrm{36}+\overset{\mathrm{2}}…

An-equilateral-triangle-inscribed-in-a-parabola-y-2-4x-One-of-its-vertices-is-at-the-vertex-of-the-parabola-Find-the-length-of-each-side-of-the-triangle-in-units-

Question Number 201660 by LimPorly last updated on 10/Dec/23 $${An}\:{equilateral}\:{triangle}\:{inscribed}\:{in}\:{a}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}.\:{One}\:{of}\:{its}\:{vertices}\:{is}\:{at}\:{the}\:{vertex}\:{of}\:\:{the}\:{parabola}. \\ $$$${Find}\:{the}\:{length}\:{of}\:{each}\:{side}\:{of}\:{the}\:{triangle}\:{in}\:{units}. \\ $$ Answered by som(math1967) last updated on 10/Dec/23 $$\:{slope}\:{of}\:{AB}\:={tan}\mathrm{30}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}…

Find-the-shortest-distance-between-point-A-3-2-and-curve-y-x-x-gt-0-

Question Number 201659 by LimPorly last updated on 10/Dec/23 $${Find}\:{the}\:{shortest}\:{distance}\:{between}\: \\ $$$${point}\:{A}\left(\mathrm{3},\mathrm{2}\right)\:{and}\:{curve}\:{y}=\sqrt{{x}}\:\left({x}>\mathrm{0}\right). \\ $$ Answered by mr W last updated on 10/Dec/23 $${say}\:{the}\:{distance}\:{is}\:{s}. \\ $$$${say}\:{the}\:{point}\:{on}\:{the}\:{curve}\:{is}\:\left({p}^{\mathrm{2}}…