In-an-xy-plane-the-graph-of-the-equation-x-6-2-y-5-2-16-is-a-circle-P-10-5-is-on-the-circle-If-PQ-is-a-diameter-of-the-circle-what-is-the-co-ordinate-at-Q-

Question Number 21925 by >>Umar << last updated on 07/Oct/17

$$\mathrm{In}\:\mathrm{an}\:\mathrm{xy}\:\mathrm{plane}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{x}−\mathrm{6}\right)^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{16}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}.\:\mathrm{P}\left(\mathrm{10},−\mathrm{5}\right) \\ $$$$\mathrm{is}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}.\:\mathrm{If}\:\mathrm{PQ}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diameter}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{co}-\mathrm{ordinate}\:\mathrm{at}\:\mathrm{Q}? \\ $$

Answered by Tinkutara last updated on 07/Oct/17

$${Center}\:{of}\:{circle},\:{C}=\left(\mathrm{6},−\mathrm{5}\right) \\ $$$${Let}\:{Q}=\left({x},{y}\right) \\ $$$${Then}\:{C}\:{is}\:{the}\:{midpoint}\:{of}\:{PQ}. \\ $$$$\therefore\:\left(\frac{\mathrm{10}+{x}}{\mathrm{2}},\frac{−\mathrm{5}+{y}}{\mathrm{2}}\right)=\left(\mathrm{6},−\mathrm{5}\right) \\ $$$$\mathrm{10}+{x}=\mathrm{12};\:{y}−\mathrm{5}=−\mathrm{10} \\ $$$${x}=\mathrm{2};\:{y}=−\mathrm{5} \\ $$

Commented by >>Umar << last updated on 07/Oct/17

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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