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GeometryQuestion and Answers: Page 89

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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.

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

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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.

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

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