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Category: Coordinate Geometry

Find-equation-of-an-ellipse-whose-major-axis-is-vertical-with-the-center-located-1-3-at-the-distance-between-the-center-and-one-of-the-covertices-equal-to-4-and-the-distance-between-the-center

Question Number 9732 by tawakalitu last updated on 29/Dec/16 $$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ellipse}\:\mathrm{whose}\:\mathrm{major}\:\mathrm{axis} \\ $$$$\mathrm{is}\:\mathrm{vertical},\:\mathrm{with}\:\mathrm{the}\:\mathrm{center}\:\mathrm{located}\:\left(−\:\mathrm{1},\:\mathrm{3}\right) \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{center}\:\mathrm{and}\:\mathrm{one}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{covertices}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{4},\:\mathrm{and}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{center}\:\mathrm{and}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vertices}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{6}. \\ $$ Answered by sandy_suhendra…

show-that-the-ellipse-with-e-5-3-focus-0-2-and-directrix-x-4-5-3-has-the-equation-x-5-2-9-y-2-2-4-1-

Question Number 9163 by tawakalitu last updated on 21/Nov/16 $$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{with}\:\mathrm{e}\:=\:\frac{\sqrt{\mathrm{5}}}{\mathrm{3}},\: \\ $$$$\mathrm{focus}\:\left(\mathrm{0},\:\mathrm{2}\right)\:\mathrm{and}\:\mathrm{directrix}\:\mathrm{x}\:=\:−\frac{\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{3}} \\ $$$$\mathrm{has}\:\mathrm{the}\:\mathrm{equation}\::\:\frac{\left(\mathrm{x}\:−\:\sqrt{\mathrm{5}}\right)^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\left(\mathrm{y}\:−\:\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{4}}\:=\:\mathrm{1} \\ $$ Commented by sandy_suhendra last updated on 22/Nov/16…

Question-9048

Question Number 9048 by tawakalitu last updated on 16/Nov/16 Answered by Rasheed Soomro last updated on 16/Nov/16 $$\left.\mathrm{a}\right)\:\:\mathrm{Straight}\:\mathrm{line}:\:\mathrm{y}=\mathrm{mx}+\mathrm{c} \\ $$$$\:\:\:\:\:\:\:\mathrm{Circle}:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{2gx}+\mathrm{2fy}+\mathrm{C}_{\mathrm{1}} =\mathrm{0} \\ $$$$\mathrm{For}\:\mathrm{intersection}\:\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{above}…

Question-8929

Question Number 8929 by kuldeep singh raj last updated on 06/Nov/16 Commented by Rasheed Soomro last updated on 06/Nov/16 $$\mathrm{This}\:\mathrm{depends}\:\mathrm{upon}\:\mathrm{the}\:\mathrm{position}\:\mathrm{of}\:\mathrm{C}. \\ $$$$\mathrm{For}\:\mathrm{example}\:\mathrm{how}\:\mathrm{far}\:\mathrm{is}\:\mathrm{C}\:\mathrm{from}\:\mathrm{A}. \\ $$$$\mathrm{So}\:\mathrm{additional}\:\:\mathrm{information}\:\mathrm{is}\:\mathrm{required} \\…

Evaluate-0-1-1-2-x-2-y-dx-y-2-x-dy-along-a-straight-line-from-0-1-to-1-2-

Question Number 139924 by EDWIN88 last updated on 02/May/21 $$\:\:\:\:\:\:\mathrm{Evaluate}\:\int_{\left(\mathrm{0},\mathrm{1}\right)} ^{\left(\mathrm{1},\mathrm{2}\right)} \:\left[\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}\right)\mathrm{dx}\:+\:\left(\mathrm{y}^{\mathrm{2}} +\mathrm{x}\right)\:\mathrm{dy}\:\right]\: \\ $$$$\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{from}\:\left(\mathrm{0},\mathrm{1}\right)\:\mathrm{to}\:\left(\mathrm{1},\mathrm{2}\right). \\ $$ Answered by TheSupreme last updated on 02/May/21…

Let-consider-I-R-2-a-parametric-curve-1-Prove-that-if-a-lt-b-and-a-b-then-there-exist-t-0-a-b-such-as-t-0-is-colinear-to-b-a-2-Show-that-if-is-regular-and-the-

Question Number 74300 by ~blr237~ last updated on 21/Nov/19 $${Let}\:{consider}\:\:\gamma\:\::{I}\rightarrow\mathbb{R}^{\mathrm{2}} \:\:{a}\:{parametric}\:{curve}\: \\ $$$$\left.\mathrm{1}\left.\right){Prove}\:{that}\:{if}\:\:{a}<{b}\:\:{and}\:\:\gamma\left({a}\right)\neq\gamma\left({b}\right)\:{then}\:{there}\:{exist}\:\:{t}_{\mathrm{0}} \in\right]{a},{b}\left[\:\:\right. \\ $$$${such}\:{as}\:\:\gamma'\left({t}_{\mathrm{0}} \right)\:\:{is}\:{colinear}\:{to}\:\gamma\left({b}\right)−\gamma\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right){Show}\:{that}\:{if}\:\:\gamma\:{is}\:{regular}\:{and}\:{the}\:\:{function}\:{f}\::{I}\rightarrow\mathbb{R}\:\:\:\:{t}\rightarrow{f}\left({t}\right)=\mid\mid\gamma\left({t}\right)−{O}\left(\mathrm{0},\mathrm{0}\right)\:\mid\mid\:\:{is}\:{maximal}\:{in}\:{t}_{\mathrm{0}} \in{I} \\ $$$${Then}\:\:\mid{K}_{\gamma} \left({t}_{\mathrm{0}} \right)\mid\geqslant\frac{\mathrm{1}}{{f}\left({t}_{\mathrm{0}} \right)}…

Prove-that-S-x-y-z-R-3-x-2-y-2-z-2-is-a-surface-and-find-out-if-possible-the-tangent-plan-in-O-0-0-0-

Question Number 74301 by ~blr237~ last updated on 21/Nov/19 $${Prove}\:{that}\:\:{S}=\left\{\left({x},{y},{z}\right)\in\mathbb{R}^{\mathrm{3}} \backslash\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={z}^{\mathrm{2}} \:\right\}\:{is}\:{a}\:{surface}\: \\ $$$${and}\:{find}\:{out}\:{if}\:{possible}\:{the}\:{tangent}\:{plan}\:{in}\:{O}\left(\mathrm{0},\mathrm{0},\mathrm{0}\right). \\ $$ Answered by mind is power last updated…