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Category: Coordinate Geometry

A-parabola-with-equation-y-x-2-k-5-intersects-a-circle-with-equation-x-2-y-2-25-at-exactly-3-points-A-B-C-Determine-all-such-positive-integers-k-for-which-the-area-of-ABC-is-an-integer

Question Number 11607 by Joel576 last updated on 29/Mar/17 $$\mathrm{A}\:\mathrm{parabola}\:\mathrm{with}\:\mathrm{equation}\:{y}\:=\:\frac{{x}^{\mathrm{2}} }{{k}}\:−\:\mathrm{5}\:\mathrm{intersects} \\ $$$$\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{25}\:\mathrm{at}\:\mathrm{exactly}\:\mathrm{3}\:\mathrm{points}\:{A},\:{B},\:{C} \\ $$$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{such}\:\mathrm{positive}\:\mathrm{integers}\:{k}\:\mathrm{for}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer} \\ $$ Answered by mrW1 last…

what-is-the-intercept-of-x-2-a-2-y-2-b-2-1-on-the-x-axis-

Question Number 11591 by agni5 last updated on 28/Mar/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intercept}\:\mathrm{of}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{x}-\mathrm{axis}\:? \\ $$ Answered by ajfour last updated on 28/Mar/17…

Show-that-the-graph-of-y-x-3-2x-2-x-1-between-x-1-and-x-2-lies-entirely-above-the-x-axis-

Question Number 11473 by tawa last updated on 26/Mar/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:,\:\mathrm{between}\:\mathrm{x}\:=\:−\:\mathrm{1}\:\mathrm{and}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{lies}\:\mathrm{entirely}\:\mathrm{above}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis} \\ $$ Commented by prakash jain last updated on 28/Mar/17 $${y}={x}^{\mathrm{3}}…

Find-equation-of-the-hyperbolas-that-intersect-3x-2-4y-2-5xy-and-3y-2-4x-2-2x-5-

Question Number 11394 by agni5 last updated on 23/Mar/17 $$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolas}\:\mathrm{that}\: \\ $$$$\mathrm{intersect}\:\mathrm{3x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} =\mathrm{5xy}\:\mathrm{and}\: \\ $$$$\mathrm{3y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}. \\ $$ Terms of Service Privacy Policy…

Find-the-equation-and-radius-of-the-circumference-of-the-triangle-formed-by-the-three-lines-2y-9x-26-0-9y-2x-32-0-11y-7x-27-0-

Question Number 11303 by tawa last updated on 19/Mar/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{formed} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{three}\:\mathrm{lines}. \\ $$$$\mathrm{2y}\:−\:\mathrm{9x}\:+\:\mathrm{26}\:=\:\mathrm{0} \\ $$$$\mathrm{9y}\:+\:\mathrm{2x}\:+\:\mathrm{32}\:=\:\mathrm{0} \\ $$$$\mathrm{11y}\:−\:\mathrm{7x}\:−\:\mathrm{27}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated…

Question-142326

Question Number 142326 by bramlexs22 last updated on 30/May/21 Answered by EDWIN88 last updated on 30/May/21 $$\:\:\frac{\mathrm{180}\left(\mathrm{n}−\mathrm{2}\right)}{\mathrm{n}}\:=\:\mathrm{4}\left(\frac{\cancel{\mathrm{180}}\:^{\mathrm{36}} }{\cancel{\mathrm{5}}}\:\right) \\ $$$$\:\frac{\mathrm{180n}−\mathrm{360}}{\mathrm{n}}\:=\:\mathrm{144}\:\Rightarrow\mathrm{180n}−\mathrm{360}=\mathrm{144n} \\ $$$$\Rightarrow\:\mathrm{36n}\:=\:\mathrm{360}\:;\:\mathrm{n}=\mathrm{10} \\ $$$$\: \\…