Question

A has center of (0, 4) and a radius of 6, and circle B has a center of (-3, 5) and a radius of 24. What steps will help show that circle A is similar to circle B?

Answer 1

Two circles are similar because they have the same shape: they are both circles.
It's difficult to see what this question is asking. Perhaps the Explanation below is what is being looked for.

Explanation:

Two shapes are similar if by applying

• translation (shift);
• dilation (resizing);
• reflection; and/or
• rotation

they can be mapped into identical forms.

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Note that

• Circle A with center `(""(0,4))` and radius `6`
  has a Cartesian equation
  `color(white)("XXX")(x-0)^2+(y-4)^2=6^2`
• Circle B with center `("(-3,5))` and radius `24`
  has a Cartesian equation
  #color(white)("XXX")(x+3)^2+(y-5)^2=24^2

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In the Cartesian plane:

translation (shift) of `color(black)(vec(""(a,b))`
Every coordinate `x` value has `a` added to it; and
every coordinate `y` value has `b` added to it.

Applications
Applying a translation of `vec(""(color(red)(0),color(blue)(4)))` to circle A
gives the circle A' with the equation:
`color(white)("XXX")((xcolor(red)(0))-0)^2+((ycolor(blue)(+4))-4)^2=6^2`
`color(white)("XXX")rarr x^2+y^2=6^2`
Applying a translation of `vec(""(color(red)(3),color(blue)(-5)))` to circle B
gives a circle B' with the equation:
`color(white)("XXX")((xcolor(red)(+3))-3)^2+((ycolor(blue)(-5))+5)^2=24^2`

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dilation of `color(black)(d)`
Distances from the origin are multiplied by `color(black)(d)`

Application
(note for the equation of a circle, only the radius is a `underline("distance")` measurement).
Applying a dilation of `4` to the equation of Circle A'
gives the circle A'' with equation
`color(white)("XXX")x^2+y^2=(6xx4)^2`
`color(white)("XXX")rarr x^2+y^2=24^2`

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Since the equations for A'' and B' are identical
and
Circle A'' is the same as Circle A after translation and dilation
and
Circle B' is the same as Circle B after translation.

`rArr` Circle A and Circle B are similar.