HOMEWORK HELPP on coordinate geometry/ circles!!

i missed a couple of days of college due to illness. i missed a section on coordinate geometry, i have mostly caught up. I'm stuck on circles bit. i feel really bad for leaving my homework to last minute. I understand how to form an equation with a centre and radius, finding the centre and radius from an equation
I honestly don't understand this...how do i find the equation from two points??

1.

The point C (-4,2) and the point A (6,3). Find the equation circle, centre C and radius CA.

2.

The points A (2,0) and B (6,4) form a diameter of a circle. find the equation of the circle

3.

A circle passes through points Q (0,3) and R (0,9) and touches the X-axis. work out two possible equations.

4.

show that y=4-x is a tangent to a circle x^2+y^2= 8

Thank you so much for your help. these are some of the questions i found hard, once i get an explanation i will apply it to other questions

Reply 1

Lunch_Box

15

Original post by safarichik

[*] The point C (-4,2) and the point A (6,3). Find the equation circle, centre C and radius CA.

You know the equation of a circle is (x-x1)^2 + (y-y1)^2 = r^2 ... centre (x1,y1) and radius r.

Therefore you know the values of x1 and y1.

To find the radius, draw a simple diagram of the circle and the point A, and you should be able to find the radius using pythagorus' theorem.

Reply 2

BlueSam3

17

In addition to the above:
For (2), find the midpoint of AB to find the centre and proceed as in (1).
For (3), find the y-coordinate of the centre using the points given, and hence its radius, then use a triangle including the centre and one of the given points to get the distance from the y axis to the centre, and note the two possible values of this (draw a diagram if you aren't sure), then proceed as in (1).
For (4), treat the two equations given as a system of simultaneous equations and show that there is only one solution.

Reply 3

safarichik

OP

Original post by BlueSam3

In addition to the above:
For (2), find the midpoint of AB to find the centre and proceed as in (1).
For (3), find the y-coordinate of the centre using the points given, and hence its radius, then use a triangle including the centre and one of the given points to get the distance from the y axis to the centre, and note the two possible values of this (draw a diagram if you aren't sure), then proceed as in (1).
For (4), treat the two equations given as a system of simultaneous equations and show that there is only one solution.

thanks

HOMEWORK HELPP on coordinate geometry/ circles!!

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