Circle A has a radius of #1 # and a center of #(5 ,2 )#. Circle B has a radius of #2 # and a center of #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

After the translation #C_B=(4-3,5+4)=(1,9)#

The distance between #C_AandC_B# can be calculated by the good old Pythagoras: #(C_AC_B)^2=(5-1)^2+(2-9)^2=16+49=65# #->C_AC_B=sqrt65~~8.06#
Since the radii of the circles add up to #3#, they don't overlap, and the minimum distance between points on the circles will be: #d=sqrt65-3~~5.06#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2
To determine if circle B overlaps circle A after being translated by <-3, 4>, we need to calculate the distance between the centers of the circles after the translation and compare it to the sum of their radii. The distance between the centers of the circles can be found using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For circle A, the center is at (5, 2), and for circle B after translation, the center becomes (4 - 3, 5 + 4) = (1, 9). \[ \text{Distance} = \sqrt{(1 - 5)^2 + (9 - 2)^2} = \sqrt{16 + 49} = \sqrt{65} \] The sum of the radii of circle A and circle B is \( 1 + 2 = 3 \). Since the distance between the centers of the circles (\( \sqrt{65} \)) is greater than the sum of their radii (3), the circles do not overlap. To find the minimum distance between points on both circles, we subtract the sum of the radii from the distance between their centers: \[ \text{Minimum distance} = \sqrt{65} - 3 \]
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7