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Category: Coordinate Geometry

Find-the-angle-at-which-the-parabola-y-x-2-cuts-through-the-line-3x-y-2-0-

Question Number 93853 by Ar Brandon last updated on 15/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{cuts}\:\mathrm{through}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}−\mathrm{y}−\mathrm{2}=\mathrm{0} \\ $$ Answered by Kunal12588 last updated on 15/May/20 $${y}={x}^{\mathrm{2}} ,\:{y}=\mathrm{3}{x}−\mathrm{2}…

If-one-line-of-the-equation-ax-3-bx-2-y-cxy-2-dy-3-0-bisects-the-angle-between-the-the-other-two-then-prove-3a-c-2-bc-2cd-3ad-b-3d-2-bc-2ab-3ad-

Question Number 28303 by ajfour last updated on 24/Jan/18 $${If}\:{one}\:{line}\:{of}\:{the}\:{equation}\:: \\ $$$$\boldsymbol{{ax}}^{\mathrm{3}} +\boldsymbol{{bx}}^{\mathrm{2}} \boldsymbol{{y}}+\boldsymbol{{cxy}}^{\mathrm{2}} +\boldsymbol{{dy}}^{\mathrm{3}} =\mathrm{0} \\ $$$${bisects}\:{the}\:{angle}\:{between}\:{the} \\ $$$${the}\:{other}\:{two}\:{then}\:{prove} \\ $$$$\left(\mathrm{3}{a}+{c}\right)^{\mathrm{2}} \left({bc}+\mathrm{2}{cd}−\mathrm{3}{ad}\right)= \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}+\mathrm{3}{d}\right)^{\mathrm{2}}…

Question-28278

Question Number 28278 by ajfour last updated on 23/Jan/18 Commented by ajfour last updated on 23/Jan/18 $${If}\:{y}={mx}+{c}\:\:\:{be}\:{tangent}\:{to}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:,\:{find}\:{the} \\ $$$${condition}\:{for}\:{tangency}\:{of}\:{the}\:…

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}…