Write x2 + y2 – 18x + 8y + 5 = 0 in standard form.

Group terms and move the constant to the other side of the equation.
x2 – 18x + y2 + 8y = –5
Determine the values that need to be added to both sides of the equation.
(–18 ÷ 2)2 = 81 and (8 ÷ 2)2 = 16
Add the values to both sides of the equation.
Write each trinomial as a binomial squared, and simplify the right side.
What is the standard form of the equation of a circle given by x2 + y2 – 18x + 8y + 5 = 0?

A circle is a curve sketched out by a point moving in a plane. The standard form of the equation is x²-18x+y²+8x=-5 is (x-9)²+(y+4)²=92.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

To solve the equation in the standard form we need to bring the equation in the form of the equation of a circle, therefore, the equation can be solved as,

[tex]x^2-18x + y^2 + 8y = -5[/tex]

Since (–18 ÷ 2)² = 81 and (8 ÷ 2)² = 16. We will add 81 and 16 on both the sides of the equation, therefore, we will get,

[tex]x^2-18x+81 + y^2 + 8y +16= -5+81+16\\\\[/tex]

Now bring the trinomial as a binomial squared form, we will get,

[tex](x^2-18x+81) + (y^2 + 8y +16)= 92\\\\(x-9)^2+(y+4)^2=92[/tex]

Thus, the standard form of the equation is x²-18x+y²+8x=-5 is (x-9)²+(y+4)²=92.

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