Question

What is the radius of the circle defined by x² + y² -4x + 8y = 7?

Answer 1

seriously?

uh posted a wrong question or incomplete question

Answer 2

Answer:

The radius of the given circle is $\sqrt{27} units$.

Step-by-step explanation:

The standard form of the equation of a circle is given by

$\big(x-a\big)^{2} +\big(y-b\big)^{2} =r^{2}$

where a, b are the respective x, y - coordinates of the circle at the center  and r is the radius of the circle.

Given the equation of a circle,

$x^2 + y^2 -4x + 8y = 7$

Grouping the like terms, we get

$\big(x^2 -4x\big)+\big( y^2 + 8y\big )= 7$

Adding 4 and 16 on both the sides, so that the x and y terms can be written in the standard form of the circle.

$\big(x^2 -4x+4\big)+\big( y^2 + 8y+16\big )= 7+4+16$

Now the terms in the brackets can be rewritten as

$\big(x -2\big)^2+\big( y +4\big )^2= 27$

Now, comparing the equation with the standard form,

the coordinates are $(a, b)=(-2, 4)$

and the radius is $r^{2} =27\implies r=\sqrt{27}$

Therefore, the radius of the given circle is $\sqrt{27} units$.

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