# Coordinate geometry questions.

• Feb 5th 2010, 05:37 PM
NitroKnight
Coordinate geometry questions.
I have a few more questions that are giving me a hard time...

1
What is the equation of the perpendicular bisector of the line between the points (2,2) an (6,6)?

2
What is the equation of a parabola with vertex (0,0) and focus (0,4)

3
Given that the equation of a circle is $x^2+y^2-10x+4y+13=0$,
find it's center and it's radius.
• Feb 5th 2010, 06:05 PM
Quote:

Originally Posted by NitroKnight
I have a few more questions that are giving me a hard time...

1
What is the equation of the perpendicular bisector of the line between the points (2,2) an (6,6)?

2
What is the equation of a parabola with vertex (0,0) and focus (0,4)

3
Given that the equation of a circle is $x^2+y^2-10x+4y+13=0$,
find it's center and it's radius.

hi

(1) first of all , get the midpoint which is (4,4) , then find the line perpendicular which passes through the midpoint . The gradient of this line would be 1 so the gradient of the line perpendicular to this line = -1 ,

y-4=-1(x-4)

y=-x+8

(2) Focus , F=(0,4) so we know that the parabola is in the form of $x^2=4ay$ , vertex is 0 so the equation would be $x^2=16y$ .

(3) The general equation is given by

$x^2+y^2+2gx+2fy+c=0$ where the radius would be (-g,-f) and the radius $= \sqrt{g^2+f^2-c}$

so for this question , 2g=-10 , g=-5 and 2f=4 , f=2

centre =(5,-2) and radius $=\sqrt{(-5)^2+(2)^2-13}=4$