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# Analytic Geometry

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Find the radius of the circle with equation x^2 - 4x + y^2 - 6y - 36 = 25

Oct 16, 2021

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Hello,

($${x}^{2}-4x+{y}^{2}-6y-36=25$$),

($$x^2-4x-y^2-6y=25+36$$),

($$x^2-4x+y^2-6y=61$$),

($$x^2-4x+?+y^2-6y=61+?$$),

to solve the equation $$x^2-4x+4=(x-2)^2$$,

($$x^2-4x+4+y^2-6y=61+4$$),

factorise the expression using square of a binomial ($$a^2-2ab+b^2=(a-b)^2$$),

$$(x-2)^2+y^2-6y=61+4$$

$$(x-2)^2+y^2-6y=65$$,

$$(x-2)^2+y^2-6y+?=65+?$$,

to solve the equation $$y^2-6y+9=(y-3)^2$$,

$$(x-2)^2+y^2-6y+9=65+9$$,

factorise the expression using square of a binomial $$a^2-2ab+b^2=(a-b)^2$$,

$$(x-2)^2+(y-3)^2=65+9$$,

$$(x-2)^2+(y-3)^2=74$$,

The equation can be written in the form $$(x-p)^2+(y-q)^2=r^2$$

so that it corresponds to a circle with radius ($$r=\sqrt{74}$$) and centre ($$2,3$$).

Straight

Oct 16, 2021