Locus and parabola question (1 Viewer)

[Sparklingstar]

A circle has centre c(-1,3) and radius 5 units.
The first two parts, a) and b) I have already done I'm just stuck on c)
a) find the equation of the circle and
b) the line 3x-y+1=0 meets the circle at the two points. Find their coordinates

C)let the coordinates be x and y, where y is the coordinate directly below the centre c, find the coordinates of point z, where yz is a diameter of the circle

Thank you.
Oh and the answer for c) is (-1,8)

 

[Jashua_Long]

A circle has centre c(-1,3) and radius 5 units.
The first two parts, a) and b) I have already done I'm just stuck on c)
a) find the equation of the circle and
b) the line 3x-y+1=0 meets the circle at the two points. Find their coordinates

C)let the coordinates be x and y, where y is the coordinate directly below the centre c, find the coordinates of point z, where yz is a diameter of the circle

Thank you.
Oh and the answer for c) is (-1,8)

It's geometrically obvious??

Draw a picture.

You don't even need parts (a) and (b) to do (c)

 

[such_such]

Yeah, it's easier if you draw a picture.

let that point be P(x,y)
but you know that it's below the centre so it becomes (-1,y)

From the c(-1,3) to the top of the circle, just add the radius to the y coordinate
= P(-1, 3+5)
= P(-1,8)

 

[nifkeh]

If y is below C, and yz forms a diameter then basically points y, z and c are in a straight line (collinear?)

So it's given to you that the radius of the circle is 5 units, which is the focal length.

so since they're all in a straight line, the x- coordinate will be the same (it's a vertical line cutting the x-axis), so you're given the coordinates for C, which is (-1,3), so the x- coordinates of y & z will be -1 as well.

For the y-coordinates of z, you just add 5 to the y-coordinate for C, which is 3, so the y-coordinate for z will be 8 => (-1,8) for the coordinates of z

coordinates of y would be (-1,-2), as it is 5 units below C.

 

[Sparklingstar]

Ooh, right right thank you!