Answer:
[tex](x+2.5)^2+(y+4.4)^2=\dfrac{49}{16}[/tex].
Step-by-step explanation:
Consider the complete question is " A circle has a radius of 7/4 units and is centered at (−2.5,−4.4). Write the equation of this circle."
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center and r is radius of the circle.
Substitute h=-2.5, k=-4.4 and r=7/4 in the above formula.
[tex](x-(-2.5))^2+(y-(-4.4))^2=(\dfrac{7}{4})^2[/tex]
[tex](x+2.5)^2+(y+4.4)^2=\dfrac{49}{16}[/tex]
Hence the equation of circle is [tex](x+2.5)^2+(y+4.4)^2=\dfrac{49}{16}[/tex].
The equation of the circle, which has a radius of 7/4 units and is centered at (−2.5,−4.4), is x²+y²+5x+8.8y=-22.5475.
The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A circle has a radius of 7/4 units and is centered at (−2.5,−4.4). Put the values in the above equation,
[tex](x-(-2.5))^2+(y-(-4.4))^2=(7/4)^2\\(x+2.5)^2+(y+4.4)^2=\dfrac{49}{16}\\x^2+5x+6.25+y^2+8.8y+19.36=3.0625\\x^2+y^2+5x+8.8y=3.0625-6.25-19.36\\x^2+y^2+5x+8.8y=-22.5475[/tex]
Thus, the equation of the circle, which has a radius of 7/4 units and is centered at (−2.5,−4.4), is x²+y²+5x+8.8y=-22.5475.
Learn more about the equation of circle here;
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