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Category: Coordinate Geometry

M-N-are-endpoints-of-a-diameter-4x-y-15-of-circle-x-2-y-2-6x-6y-16-0-and-are-also-on-the-tangents-at-the-end-points-of-the-major-axis-of-an-ellipse-respectively-such-that-MN-is-also-tangent-to

Question Number 28185 by ajfour last updated on 21/Jan/18 $${M},\:{N}\:{are}\:{endpoints}\:{of}\:{a}\:{diameter} \\ $$$$\:\mathrm{4}{x}−{y}=\mathrm{15}\:\:{of}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}{y}−\mathrm{16}=\mathrm{0}\:;\:{and}\:{are} \\ $$$${also}\:{on}\:{the}\:{tangents}\:{at}\:{the}\:{end} \\ $$$${points}\:{of}\:{the}\:{major}\:{axis}\:{of}\:{an} \\ $$$${ellipse}\:{respectively},\:{such}\:{that} \\ $$$${MN}\:{is}\:{also}\:{tangent}\:{to}\:{the}\:{same} \\…

Question-159180

Question Number 159180 by cortano last updated on 14/Nov/21 Answered by som(math1967) last updated on 14/Nov/21 $${HI}=\mathrm{50}{tan}\mathrm{48}=\mathrm{55}.\mathrm{53} \\ $$$${HL}=\mathrm{55}.\mathrm{53}+\mathrm{40}=\mathrm{95}.\mathrm{53} \\ $$$${LQ}=\mathrm{50}+\mathrm{8}=\mathrm{58} \\ $$$${HQ}=\sqrt{\mathrm{58}^{\mathrm{2}} +\left(\mathrm{95}.\mathrm{53}\right)^{\mathrm{2}} }=\mathrm{111}.\mathrm{75}\:{feet}\left({approx}\right)…

Question-159135

Question Number 159135 by cherokeesay last updated on 13/Nov/21 Commented by Rasheed.Sindhi last updated on 13/Nov/21 $${I}'{ve}\:{now}\:{understood}\:{completely}\: \\ $$$${although}\:\:{difficultly}. \\ $$$${I}\:{want}\:{to}\:{say}\:{only}\:{that}\:{the}\:{answer} \\ $$$${should}\:{be}\:{somewhat}\:{more}\:{detailed} \\ $$$${in}\:{order}\:{that}\:{the}\:{persons}\:{who}\:{are}…

Question-27818

Question Number 27818 by ajfour last updated on 15/Jan/18 Commented by ajfour last updated on 15/Jan/18 $${If}\:{y}={Ax}^{\mathrm{2}} \:{is}\:{reflected}\:{in}\:{the}\:{line} \\ $$$$\frac{{x}}{{a}}+\frac{{y}}{{b}}=\mathrm{1}\:,\:{find}\:{equation}\:{of}\:{its} \\ $$$${reflection}\:{f}\left({x},{y}\right)=\mathrm{0}\:. \\ $$ Commented…

Question-158143

Question Number 158143 by alcohol last updated on 31/Oct/21 Commented by TheHoneyCat last updated on 31/Oct/21 $$\mathrm{G}_{\mathrm{3}} \:\mathrm{and}\:\mathrm{G}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{clearly}\:\mathrm{isomorphical}\:\mathrm{buy}\:\mathrm{looking} \\ $$$$\mathrm{at}\:\mathrm{their}\:\mathrm{respectiv}\:\mathrm{tables}. \\ $$$$\mathrm{we}\:\mathrm{just}\:\mathrm{need}\:\mathrm{to}\:\mathrm{map}\:\mathrm{as}\:\mathrm{follow}: \\ $$$$\begin{cases}{\mathrm{1}}&{\leftrightarrows}&{\mathrm{1}}\\{\mathrm{5}}&{\leftrightarrows}&{\mathrm{3}}\\{\mathrm{7}}&{\leftrightarrows}&{\mathrm{5}}\\{\mathrm{11}}&{\leftrightarrows}&{\mathrm{7}}\end{cases}…