Question

Determine the equation for a circle with radius 5, center on the line 5x=2y, and tangent to the X axis

Answer 1

need help guys???? please

Answer 2

@Yahoo! @surdawi Please Help!

Answer 3

Start with the given equation.

Answer 4

@Yahoo! Please help :)

Answer 5

@ayman171819 Did you try to solve the ques ?

Answer 6

let the circle is (a,b) can you state a in term of b or vice versa ? *hint:center on the line 5x=2y
the circle tangent to x-axis, so the radius equals to b, why?

Answer 7

what should be do??? it just multi chose

Answer 8

I'll but the chose

Answer 9

(x-2)^2 + (y-1)^2=8
(x-2)^2 + (y-5)^2=25
(x+2)^2 + (y-5)^2=25
(x+2)^2 + (y+1)^2=8

Answer 10

first, you have to find the centre of the circle,
can you find the value of a and b, from the explanation that I gave before?

Answer 11

what you gave me, I did not understand it. it kind of hard!!

Answer 12

@ayman171819 Do you understand the meaning of tangent?

Answer 13

yes I do but the instructor make it difficult... I want help???

Answer 14

Remember that your circle is solely defined by a radius and a center. You already have a radius, all that's left is for you to define the point (a,b) which is its center.

Answer 15

Let test if you know it, how long is the distance between x axis and the center?

Answer 16

is 5

Answer 17

Very good, but why?

Answer 18

from the origin??

Answer 19

yes

Answer 20

Ok, basics time :D
Your circle has a general equation
\[r^{2}=(x - h)^{2}+(y-k)^{2}\]
where
r = radius
(h, k) is the center of your circle
You just have to fill in for r, h, and k.
You already know
r = 5 (right?)
Do you know how to get started in finding h and k?

Answer 21

I know the formula.. but the question is
Determine the equation for a circle with radius 5, center on the line 5x=2y, and tangent to the X axis. how to find H,K ??/

Answer 22

I did circles questions but this is kind of tricky one

Answer 23

Well, you have two unknowns, it'd be nice to find two linear equations that involve those two unknowns :D
Ok, so h is the x-value for your centre, and k is the y-value for your centre.
Your conditions specify that your centre is on the line 5x = 2y, so regardless of the x and y, they must satisfy that equation.
So
5h = 2k
Do you understand why?

Answer 24

Hint: center ( h, k) with:
h is the distance between center and y axis
k ........................................................x axis !

Answer 25

what i understood it gunna be the equation like this (x-5)^2 + (y-2)=25

Answer 26

And you already know " Let test if you know it, how long is the distance between x axis and the center? "

Answer 27

5,2

Answer 28

Hey, if you have time, it might be prudent to pretend that there are no choices for this one. Sooner or later, you might have to find the equation of a circle without any.

Answer 29

terenzreignz's so right about it! Do it yourself without looking at the given optional choices :)

Answer 30

Back to our findings
Your centre is the point (h, k) right?
We don't know what h and k are, but we do know that (h, k) is on the line 5x = 2y
So, can you form an equation that relates h and k?

Answer 31

(x-5)^2 + (y-2)=25

Answer 32

or should be first make it like this 5x-2y=0 ????

Answer 33

Let's not jump to conclusions :D
(And by the way, that answer is not in your choices...)

We know that (h, k) satisfies the condition 5x = 2y, right?

Answer 34

yes

Answer 35

Well, what does that tell you about h and k?

Answer 36

H= 5,, K=2

Answer 37

No. Ok, let's be more direct.
(12, 30) satisfies the equation 5x = 2y
BECAUSE
5(12) = 2(30)
So, if (h, k) satisfies 5x = 2y as well, then...?

Answer 38

60=60 is equal

Answer 39

Ok. But other than that, what does it tell you about h and k?

Answer 40

h=0. k=0.. because we do not have square

Answer 41

No. Ok, let's just get down to it.
(h, k) satisfies the equation 5x = 2y
THEREFORE
5h = 2k

Answer 42

Just like I did with the (12, 30) example

Answer 43

ok

Answer 44

Now, that does not tell you enough to give specific values for h and k.
The task is to find another equation that involves h or k, or perhaps both, so that you have a system of equations (or simpler). Go ahead find one.

Answer 45

you mean to make the same original equation

Answer 46

No, I mean find an equation so that you can determine the values of h and k. You have
5h = 2k, but one equation is not enough, as you have two unknowns. Acquire another one.

Answer 47

(x-5)^2 + (y-2)

Answer 48

Well, I'll hear you out; How did you come by that solution?

Answer 49

Which, by the way, is not an equation, don't forget the = 25

Answer 50

and the ^2 on the (y - 2)

Answer 51

(x-5)^2 + (y-2)^2=25 this is the final answer or what???

Answer 52

Of course not. It's not even in your choices.

Answer 53

(x-5)^2 + (y-2)^2=25
this is one of the choices

Answer 54

I think that's not the answer.
(Don't agree with me? Prove me wrong :P)
But seriously, if you really think that that's the answer, then please show how you got it.

Answer 55

if I'm wrong teach me how get the answer..

Answer 56

I am. Just follow on, and avoid jumping to conclusions. We know that
5h = 2k
right?
Let's put that to one side.
The circle is tangent to the x-axis, right? Do you have an idea what that looks like?

Answer 57

You've already known r = 5 and k = ....?
Then from 5h = 2k -> h = ....?
Then plug into ( x - h)² + ( y - k)² = r²

Answer 58

(x-5)^2 + (y-2)^2=25 like this

Answer 59

I don't how to draw in Computer

Answer 60

Again, please avoid jumping to conclusions. Patience...

As you can see, the circle touches the horizontal (x) axis at ONLY one point. That's what we mean by tangent.

Answer 61

Let's take a closer look, then? Oh, and borrow @chihiroasleaf 's drawing

Answer 62

@ayman171819 Don't be confused between h and k distance!

Answer 63

ok

Answer 64

What is the length of that black line I drew?

Answer 65

half

Answer 66

Half? Half of what?

Answer 67

of the circle

Answer 68

That's not very precise, is it...?
More like half its diameter.
Now, half a circle's diameter is its...?

Answer 69

@ayman171819 Imagine connecting the center to y axis --> k distance!

Answer 70

I do not have Math Vocabulary because the is my second language

Answer 71

Well, think about it. That line I drew, it's from the center to a point on the circle, that's the radius, isn't it?