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Score for Question 2: ___ of 5 points) 2. Write the equation of the circle in general form. Show your work.

Sagot :

MrRoyal

Answer:

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

Step-by-step explanation:

Given

See attachment for circle

Required

The circle equation

First, we get the radius of the circle.

From the attachment, we have:

[tex]r = 3[/tex]

Next, the center of the circle

[tex](h,k) = (-1,1)[/tex]

The equation of the circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

This gives:

[tex](x - -1)^2 + (y - 1)^2 = 3^2[/tex]

[tex](x +1)^2 + (y - 1)^2 = 3^2[/tex]

Expand

[tex]x^2 + 2x + 1 + y^2 - 2y + 1 = 9[/tex]

Collect like terms

[tex]x^2 + y^2 + 2x - 2y + 1 + 1 - 9 = 0[/tex]

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

Hence, the equation in general form is:

[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]

View image MrRoyal
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