Question

What is the radius of a circle whose equation is (x + 5)2 + (y - 3)2 = 42?

O 2 units
Ο Ο Ο
4 units
8 units
16 units

Answer 1

The radius of the circle is:

• 
  `r=4` units

Explanation:

Given the equation

`\left(x\:+\:5\right)^2\:+\:\left(y\:-\:3\right)^2=\:42`

As we know that

`\left(x\:-\:a\right)^2\:+\:\left(y\:-\:b\right)^2=\:r^2\:`

is the equation of the circle with a radius 'r', centered at (a, b)

`\mathrm{Rewrite}\:\left(x+5\right)^2+\left(y-3\right)^2=4^2\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}`

so, the circle properties are:

`\left(x-\left(-5\right)\right)^2+\left(y-3\right)^2=4^2`

Therefore, the radius of the circle is:

`r=4` units