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Write the equation of the circle in standard form. Find the center, radius, intercepts,...

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saj-94 | Salutatorian

Posted September 24, 2013 at 7:54 AM via web

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Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle.

x^2+y^2+14x-12y = 76

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 24, 2013 at 8:06 AM (Answer #1)

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`x^2+y^2+14x -12y = −76`

`x^2+14x+49-49+y^2-12y+36-36 = -76`

`(x^2+14x+49)+(y^2-12y+36)-49-36 = -76`

`(x^2+14x+49)+(y^2-12y+36)-85 = -76`

`(x^2+14x+49)+(y^2-12y+36) = -76+85`

`(x^2+14x+49)+(y^2-12y+36) = 9`

`(x+7)^2+(y-6)^2 = 3^2`

So the standard form of the circle is;

`(x+7)^2+(y-6)^2 = 3^2`

The circle with center (h,k) and radius r can be given in standard form as `(x-h)^2+(y-k)^2 = r^2`

Center coordinates (-7,6).

Radius = 3

For x intercept y = 0

`x^2+y^2+14x-12y = −76`

`x^2+14x = -76`

`x^2+14x+76 = 0`

Discriminant `= (-14)^2-4xx1xx76 = 196-304 = -108 < 0`

So there is no x intercept.

For y intercept x = 0

`x^2+y^2+14x -12y = −76`

`y^2-12y = -76`

`y^2-12y +76 = 0`

Discriminant `= (-(-12))^2-4xx1xx76 = 144-304 = -240 < 0`

So there is no y intercept.

Circle is attached in the image.

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