# Thread: CENTRE OF CIRCLE: missed lesson plz help

1. ## CENTRE OF CIRCLE: missed lesson plz help

PLZ GIVE EXPLANATIONS AND ANSWERS ASAP

questions..
The circle C with centre (a,b) and radius 5 touches x-axis at (4,0)

need to find the values of a and b

find cartesian equation for C

A tangent to the circle, drawn from point p(8,17) touches the circle T

find the length of PT to 3sf

2)

the point A has cooridinates 2,5 and point b has coordinates (-2,8)
find in cartesian form and equation of the circle with diamitar AB

PLZ GIVE EXPLANATIONS AND ANSWERS ASAP

2. Originally Posted by sasha9193
PLZ GIVE EXPLANATIONS AND ANSWERS ASAP

questions..
The circle C with centre (a,b) and radius 5 touches x-axis at (4,0)

need to find the values of a and b

find cartesian equation for C
All circles can be written as x^2 + y^2 = r^2.
This is a circle centered about the origin (0,0) with radius r.
A circle of at (3,-1) would be (x-3)^2 + (y+1)^2 = r^2
The same circle with diameter 2 would be (x-3)^2 + (y+1)^2 = 4

In your problem, you should draw out the circle.
There are two possible circles.
One that is below the x-axis, but touches at (4,0), and one that is above the x-axis, but touches at (4,0).
You have a radius of 5, so for one circle, go up 5 in the y-direction, and for the other, go down 5 in the y-direction.

The centers (a,b) would be (4,5) and (4,-5).
You know how to write these now:
A circle at (4,5) would be (x-4)^2 + (y-5)^2 = r^2
A circle at (4,-5) would be (x-4)^2 + (y+5)^2 = r^2
And you know the radius is 5, so r^2 equals (5^2) equals 25.
A circle at (4,5) with radius 5 would be (x-4)^2 + (y-5)^2 = 25
A circle at (4,-5) with radius 5 would be (x-4)^2 + (y+5)^2 = 25
^Cartesian equations.

3. So y=0 is a tangent line to the circle. With means y=0 is perpendicular to its radius so the radius has the equation x=k for some number k. Since it intersects at (4,0) it means the perpendicular radius is x=4. So on the line x=4 we can find the center (a,b). Thus, a=4 because x is fixed at 4 and we need to solve for b. Now (a,b)=(4,b) must be 5 units away from (4,0) as the problem says so b=5 or -5. Thus, (4,5) or (4,-5) are the possible centers.

4. the circle has a piccy on my question, its centre sits above the x axis and right from the y axis

5. ok plz help with rest of question, i can do up to the second one, the equation need to know rest

6. Originally Posted by sasha9193
the circle has a piccy on my question, its centre sits above the x axis and right from the y axis
Then use this:
A circle at (4,5) with radius 5 would be (x-4)^2 + (y-5)^2 = 25
(it is above the x-axis and right of the y-axis)

7. Originally Posted by sasha9193
ok plz help with rest of question, i can do up to the second one, the equation need to know rest
the point A has cooridinates 2,5 and point b has coordinates (-2,8)
find in cartesian form and equation of the circle with diamitar AB

Make a diagram. Plot point A and point B.

Note that the distance between point A and point B is:
SquareRoot(( [2-(-2)]^2 + [8-5]^2 ))
SquareRoot(( 4^2 + 3^2 ))
SquareRoot(( 16 + 9 ))
SquareRoot(( 25 ))
5

So the diameter is 5. Therefore the radius is 5/2.

Find the midpoint between A and B.
(-2,8) and (2,5) where they are in form (x,y)
The midpoint of the x's is (-2 + 2)/2
The midpoint of the y's is (8 + 5)/2

So the midpoint is: (0,13/2)

And the midpoint is the center of the circle.

Given what you've been taught about cartesian form, the answer is therefore:

(x-0)^2 + (y-13/2)^2 = (5/2)^2
x^2 + (y-13/2)^2 = 25/4
or
4(x^2) + 4(y-13/2)^2 = 25

I personally prefer the second way better.

### the circle c, with

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