Math

posted by .

Write the standard form of the equation for the circle that passes through the points (2, 6), (-4, 6), and (-4, -2). Then identify the center and radius.

So far I got

2D+6E+F+40
-4D+6E+F+52
-4D-2E+F-20

IS this correct> and how do I solve it?

• Math -

The standard form of a circle centred at (x0,y0) with a radius of r is given by:

(x-x0)²+(y-y0)²=r² ...(1)

method 1: algebraic
Given the three points, we can substitute (x1,y1) in equation to obtain an equation in x0,y0 and r.
Substituting the other two points will give two more equations which should enable us to solve for x0, y0 and r.

method 2: geometric
Take any two of the three points as a chord of the circle. Find the perpendicular bisector of the segment, L1. Take the third point together with one of the two previous points and make another perpendicular bisector, L2.
The intersection of L1 and L2 will be the centre O (x0,y0) of the circle.
Find the radius r which is the distance of O to one of the three given points.
The unknowns of equation (1) are now all known.

method 3: by determinant
The equation of the circle is given by expanding the following determinant (columns unfortunately not lined up):
x²+y² x y 1
x1²+y1² x1 y1 1
x2²+y2² x2 y2 1
x3²+y2² x3 y3 1

Using method 3, I get
(x+1)²+(y-2)²=5²

Similar Questions

2. Math(is this correct?)

Write the standard form of the equation of the circle that passes through (0,4) and has its center at (-3, -1) (x+3)^2+(y+1)^2=sqrt34

Write the standard form of the equation of a circle that passes through the points at (0,8) (8,0) and (16,8). Then identify the center and radius of the circle. (x-8)^2 + (y-8)^2 = 64 (x^2 / 64) + (y^2 / 64) = 64 center=(8,8) radius=8 …
4. Math

Write the standard form of the equation of the circle that passes through (0,4)and has its center at (-3,-1).
5. Math

Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle.
6. Math

The standard form of a circle is Ax^2+Cy^2+Dx+Ey+F=0. Write the equation for the circle: Center (1,2), point on the circle (-2,-1). Okay, I've always put circles in the form (x-h)^2+(y-k)^2=0. I got this: r^2=(x-1)^2+(y-2)^2 then I …
7. Math

These questions that I have completed are on a test review for my exam and I would just like to know if they are correct. These are only a few of the questions, I have more that are just not complete yet. Thank You! 1) List the intercepts …
8. Equations of a Circle

Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle. I have r=8, center=(8,8). What now?
9. Calculus

Complete the square to write the equation x^2 + y^2 - 6x - 2y + 4 = 0 in standard form. Use the standard form of the equation to identify the center and the radius of the circle.
10. geometry

I would love for someone to check my work on the seven problems that I did. I would be eternally grateful. I am going to list my problems and answers. Even if you only want to check one of them, that would be great. 1. Write an equation …

More Similar Questions