Question

2

A circle has the equation x^2+ y^2 + 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.

Answer 1

a) (-3, 4) and radius = 2.

b) 7 cms.

Explanation:

x^2+ y^2 + 6x - 8y + 21 = 0

x^2 + 6x + y^2 - 8y = -21

Completing the square on the x and y terms:

(x + 3)^2 - 9 + (y - 4)^2 - 16 = -21

(x + 3)^2 + (y - 4)^2 = -21 + 9 + 16 = 4

a) So the center is (-3, 4) and the radius = sqrt4 = 2.

Ill come back to you later with the second part.

(b) For the point P to be a maximum distance from the origin the line must pass through the center of the circle:

Distance of the center from origin:

= √(-3 - 0)^2 + (4 -0)^2)

= 5.

So the dsitance of P from the origin is 5 + radius

= 7 cm.