Coordinate Geometry C2 Help Needed

I need help with quite a few questions lol :P thanks to anyone who helps and person who does most i will rep :smile:

This is the first one:

A circle has the equation x2 + y2 + 6x − 8y + 21 = 0.

a) Find the coordinates of the centre and the radius of the circle.
The point P lies on the circle.
b) Find the greatest distance of P from the origin.

Reply 1

AlphaNumeric

(x+3)² = x²+6x+9
(y-4)² = y²-8x+16

(x+3)²+(y-4)² = x²+6x+y²-8x+25

Therefore (x+3)²+(y-4)²-4 = x²+6x+y²-8x+21

So (x+3)²+(y-4)² -4 = 0 means (x+3)²+(y-4)² = 2²

Therefore centre at (-3,4) with radius 2.

For part b, try drawing a line through the origin and the centre of the circle and seeing where it intersects the circle.

Reply 2

Fenchurch

Ty - heres the next lol

Circle C1 has the equation x2 + y2 − 2ay = 0, where a is a positive constant.

Find the coordinates of the centre and the radius of C1.
Circle C2 has the equation x2 + y2 − 2bx = 0, where b is a constant and b > a.

Reply 3

meef cheese

When the equation of a circle is in the form:

x2 + y2 + 2gx + 2fy + c

Centre (-g, -f)

Radius = Sqrt(g2 + f2 -c)

Reply 4

breakdance

For the first question part b:
If the point P lies on the circle its distance must be equal to the radius of the circle. Therefore maximum distance is root4=2.