The radius of the circle whose equation is [tex]x^2 + y^2 + 10x -4y -20 =0[/tex] is evaluated being of 7 units.
What is an equation of a circle?
A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
For the considered case, the equation of the circle is given as:
[tex]x^2 + y^2 + 10x -4y -20 =0[/tex]
Converting it to standard form, we get:
[tex]x^2 + y^2 + 10x -4y -20 =0\\\\x^2 +10x + 25 + y^2 -4y+ 4 -49 = 0\\\\(x+5)^2 + (y-2)^2 = 49\\\\(x-(-5))^2 + (y-2)^2 = 7^2[/tex]
Thus, comparing it with [tex](x-h)^2 + (y-k)^2 = r^2[/tex] gives us:
Center of the circle is at (-5, 2)
The radius of the circle is of 7 units.
(we can't write [tex]49 = (-7)^2[/tex] since then that would make the radius as negative which can't happen as radius represent length which is a non-negative quantity).
Thus, the radius of the circle whose equation is [tex]x^2 + y^2 + 10x -4y -20 =0[/tex] is evaluated being of 7 units.
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