Question

If the equation of a circle is (x + 4) 2 + (y - 6) 2 = 25, its radius is

Answer 1

its in the standars format of :
(x-h)^2 + (y-k)^2 = r^2
where (h,k)-centre
r- radius

So what will be the answer?

Answer 2

x=−y+ 29/2

Answer 3

hope that helped.

Answer 4

Could you walk me through how to get the answer? Everything about geometry confuses me... @studio-games @priyar

Answer 5

Let's solve for x.
(x+4)(2)+(y−6)(2)=25
Step 1: Add 4 to both sides.
2x+2y−4+4=25+4
2x+2y=29
Step 2: Add -2y to both sides.
2x+2y+−2y=29+−2y
2x=−2y+29
Step 3: Divide both sides by 2.

Answer 6

2x/2 = −2y+29/2
x= −y + 29/2

Answer 7

There you go.

Answer 8

My answers could either be one of the following: 5, 10, or 25

Answer 9

Does that change the way I need to solve the problem?

Answer 10

@queenof17 do you know the distance formula

If I wrote \[5=\sqrt{(x-(-4))^2+(y-6)^2}\]
could you tell me the distance between (x,y) and (-4,6) ?

Answer 11

Could you explain how I would go about solving it?

Answer 12

@freckles

Answer 13

do you know the distance formula?

Answer 14

\[\text{The distance from } \\ (x_1,y_1) \text{ to } (x_2,y_2) \\ \text{ is given by } d \\ \text{ in } \\ d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

Answer 15

Any point (x,y) on a circle has the same distance from the center of the circle
This distance is known as the radius

Answer 16

Okay, so what would I do first to solve it?

Answer 17

we have
\[5=\sqrt{(x-(-4))^2+(y-6)^2} \\ \text{ looking at this } \\ \text{ can you tell me the distance from } \\ (x,y) \text{ to } (-4,6)\]

Answer 18

compare this to the distance formula I wrote above

Answer 19

Was I supposed to get 20 and 36

Answer 20

are you comparing
\[5=\sqrt{(x-(-4))^2+(y-6)^2} \\ \text{ to } \\ d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

I'm asking you for the distance between (x,y) and (-4,6)


\[\text{ the first equation says the distance between } (x,y) \text{ and } (-4,6) \text{ is ....}\]

\[\text{ the second equation says the distance between } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is } d
\]

Answer 21

what is in place of d in the first equation?

Answer 22

5,

Answer 23

yes!

Answer 24

Afraid we're going into far more detail here than is ncessary!

You are given " (x + 4) 2 + (y - 6) 2 = 25 " and can / must rewrite this as

\[(x+4)^2+(y-6)^2=25=5^2\]

Answer 25

the distance between any point (x,y) and (-4,6) is 5

Answer 26

compare this to the general equation of a circle:\[(x-h)^2+(y-k)^2=r^2\]

Answer 27

Simply by doing so, you can immediately see what the value of r is. Try it.
(h,k) represents the center of the circle, by the way.

Answer 28

@mathmale I think @priyar tried that approach of just comparing to (x-h)^2+(y-k)^2=r^2
that is why I tried something else

Answer 29

I just need a step by step on how to solve the problem. I'm awful at geometry and I have a lot of problems like this

Answer 30

If you want to learn a different way of solving this problem, go ahead. I don't see any particular advantage in using the distance formula here, but it is certainly applicable. Again I think you're making this problem overly complicated.

Answer 31

I just gave you a "step by step" approach. Compare YOUR equation with the STANDARD equation; you can read off the radius, r, immediately.

Answer 32

I am, I just can't see how the number 25 is brought in

Answer 33

Again, I'm not great at geometry

Answer 34

Why do more than that if it's not necessary?

You are GIVEN that 25. That 25 is the SQUARE of the radius. Thus, the radius is 5. End of discussion.

Kindly STOP that "I'm not great at geometry" stuff. What do you hope to accomplish by saying that? Give yourself credit for your intelligence and ability to learn.

Answer 35

Please, move on to another problem. Post it separately from this one.