What is the standard form of the equation of a circle with centre (3,-1) and which touches the y-axis?

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What is the standard form of the equation of a circle with centre (3,-1) and which touches the y-axis?

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Answer 1 · 2018-08-01T14:47:25

${(x - 3)}^{2} + {(y + 1)}^{2} = 9$ $(x-3)^2+(y+1)^2=9$

or $x^{2} + y^{2} - 6 x + 2 y + 1 = 0$ $x^2+y^2-6x+2y+1=0$ in quadratic form.

Explanation:

As circle with center $(3, - 1)$ $(3,-1)$ touches $y$ $y$ -axis, its radius is equal to its abscissa i.e. $3$ $3$ , and hence standard form of the equation of circle is

${(x - 3)}^{2} + {(y - (- 1))}^{2} = 3^{2}$ $(x-3)^2+(y-(-1))^2=3^2$

or ${(x - 3)}^{2} + {(y + 1)}^{2} = 9$ $(x-3)^2+(y+1)^2=9$

or $x^{2} - 6 x + 9 + y^{2} + 2 y + 1 = 9$ $x^2-6x+9+y^2+2y+1=9$

or $x^{2} + y^{2} - 6 x + 2 y + 1 = 0$ $x^2+y^2-6x+2y+1=0$

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What is the standard form of the equation of a circle with centre (3,-1) and which touches the y-axis?

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