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GeometryQuestion and Answers: Page 90

Question Number 59987    Answers: 0   Comments: 0

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A circle x^2 +y^2 −2x−4y−5=0 with centr 0 is cut by a line y=2x+5 at points P and Q. Show that QO is perpendicular to PO.

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2x}−\mathrm{4y}−\mathrm{5}=\mathrm{0}\:\mathrm{with}\:\mathrm{centr} \\ $$$$\mathrm{0}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a}\:\mathrm{line}\:\mathrm{y}=\mathrm{2x}+\mathrm{5}\:\mathrm{at}\:\mathrm{points}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{QO}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{PO}. \\ $$

Question Number 59181    Answers: 1   Comments: 1

Question Number 59100    Answers: 1   Comments: 4

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Question Number 58986    Answers: 1   Comments: 3

Question Number 58984    Answers: 1   Comments: 0

ABCD is a square, AC is a diagonal. If the coordinate of A, C are (− 5, 8) and (7, − 4) . Find the coordinate of B and D.

$$\mathrm{ABCD}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{square},\:\mathrm{AC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diagonal}.\:\mathrm{If}\:\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{C} \\ $$$$\mathrm{are}\:\:\left(−\:\mathrm{5},\:\mathrm{8}\right)\:\mathrm{and}\:\left(\mathrm{7},\:−\:\mathrm{4}\right)\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\:\mathrm{B}\:\mathrm{and}\:\mathrm{D}. \\ $$

Question Number 58979    Answers: 1   Comments: 1

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Question Number 58567    Answers: 0   Comments: 1

A regular polygon of (2k+1) sides has 140 as the size of each interior angle.Find k

$$\:{A}\:{regular}\:{polygon}\:{of}\:\left(\mathrm{2}{k}+\mathrm{1}\right)\:{sides} \\ $$$${has}\:\mathrm{140}\:{as}\:{the}\:{size}\:{of}\:{each}\:{interior} \\ $$$${angle}.{Find}\:{k} \\ $$

Question Number 58512    Answers: 1   Comments: 1

Question Number 58493    Answers: 1   Comments: 0

Question Number 58282    Answers: 1   Comments: 0

A circle tangents to :x and y axes and x^(1/2) +y^(1/2) =a^(1/2) .find its radious.

$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{tangents}}\:\boldsymbol{\mathrm{to}}\::\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{axes}}\:\boldsymbol{\mathrm{and}} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\mathrm{2}}} +\boldsymbol{\mathrm{y}}^{\frac{\mathrm{1}}{\mathrm{2}}} =\boldsymbol{\mathrm{a}}^{\frac{\mathrm{1}}{\mathrm{2}}} .\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{radious}}. \\ $$

Question Number 57949    Answers: 0   Comments: 0

(0,i,j) is orthonormal A and B are two points wich verify AB =3 find the locus of point M wich verify MA +MB =6

$$\left(\mathrm{0},{i},{j}\right)\:{is}\:{orthonormal}\:\:\:{A}\:{and}\:\:{B}\:{are}\:{two}\:{points}\:{wich}\:{verify}\:{AB}\:=\mathrm{3} \\ $$$${find}\:\:{the}\:{locus}\:{of}\:{point}\:{M}\:{wich}\:{verify}\:\:{MA}\:+{MB}\:=\mathrm{6}\: \\ $$

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