Question-122173

Question Number 122173 by help last updated on 14/Nov/20

Answered by physicstutes last updated on 14/Nov/20

Centre lies on the line y = 1 ⇒ y−coordinate of the centre is 1. The radius of the circle is = 4 Let the x−coordinate of the centre = a Then the equation of the circle is given as S : (x−a)^2 + (y−1)^2 = 4^2 The circle passes through the point (2,3) which means this point satisfies S. ⇒ S: (2−a)^2 + (3−1)^2 = 4^2 All we are left with is to solve for a. Check with , a = 2. ⇒ coordinate of centre C(2,1) key A.

$$\:\mathrm{Centre}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{line}\:{y}\:=\:\mathrm{1}\:\Rightarrow\:{y}−\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{centre}\:\mathrm{is}\:\mathrm{1}.\: \\ $$$$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{is}\:=\:\mathrm{4} \\ $$$$\mathrm{Let}\:\mathrm{the}\:{x}−\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\:\mathrm{centre}\:=\:{a} \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{given}\:\mathrm{as} \\ $$$$\:{S}\::\:\left({x}−{a}\right)^{\mathrm{2}} \:+\:\left({y}−\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{4}^{\mathrm{2}} \\ $$$$\mathrm{The}\:\mathrm{circle}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\mathrm{3}\right)\:\mathrm{which}\:\mathrm{means} \\ $$$$\mathrm{this}\:\mathrm{point}\:\mathrm{satisfies}\:{S}. \\ $$$$\Rightarrow\:\:{S}:\:\left(\mathrm{2}−{a}\right)^{\mathrm{2}} \:+\:\left(\mathrm{3}−\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{4}^{\mathrm{2}} \\ $$$$\mathrm{All}\:\mathrm{we}\:\mathrm{are}\:\mathrm{left}\:\mathrm{with}\:\mathrm{is}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{for}\:{a}. \\ $$$$\mathrm{Check}\:\mathrm{with}\:,\:{a}\:=\:\mathrm{2}. \\ $$$$\Rightarrow\:\mathrm{coordinate}\:\mathrm{of}\:\mathrm{centre}\:{C}\left(\mathrm{2},\mathrm{1}\right)\:\: \\ $$$$\mathrm{key}\:\mathrm{A}. \\ $$

Facebook Tweet Pin

Leave a Reply Cancel reply