0
What is the centre and its radius of a circle that passes through the points of 6 3 and -5 2 and 7 2 on the Cartesian plane showing all work from start to finish?
General equation of a circle: x^2 +2gx +y^2 +2fy +c = 0
Points: (6, 3) (-5, 2) (7, 2)
Substitute the points into the general equation to form simultaneous equations:-
!2g+6f+c = -45
-10g+4f+c = -29
14g+4f+c = -53
Solving the above simultaneous equations: g = -1, f = 3 and c = -51
Therefore: x^2 -2x +y^2 +6y -51 = 0
Completing the squares of x and y: (x-1)^2 + (y+3)^2 -1-9-51 = 0
So it follows: (x-1)^2 + (y+3)^2 = 61
Centre of the circle is at (1, -3) and its radius is the square root of 61
What else can I help you with?
What is the centre and radius of a circle passing through the points of 5 5 and 8 5 and 5 1 on the Cartesian plane?
Using the formula of x^2 +2gx +y^2 +2fy +c = 0 it works out that the centre of the circle is at (6.5, 3) and its radius is 2.5 units in length. Alternatively plot the points on the Cartesian plane to find the centre and radius of the circle.
What is the centre and area in cm of a circle whose circumference cuts through the points of 1 0 and 7 -6 and 7 0 on the Cartesian plane?
It works out that the centre of the circle is at (4, -3) on the Cartesian plane and its area is 56.549 square cm rounded up to three decimal places.
What is the centre and radius of a circle that passes through the points of 2 0 and 3 1 and -6 10 on the Cartesian plane?
The equation of the circle works out as: (x+2)^2 + (y-5)^2 = 41 The circle's centre is at: (-2, 5) Its radius is the square root of 41
What is the radius of a circle and its centre that passes through the points of 5 0 and 3 4 and -5 0 on the Cartesian plane?
Points: (5, 0) and (3, 4) and (-5, 0) Equation works out as: x^2+y^2 = 25 Radius: 5 units in length Centre of circle is at the point of origin (0, 0) on the Cartesian plane.
What is the distance that passes through the centre of a circle called?
It is the diameter of the circle.
What is the centre and radius of a circle enscribed through the points of 6 2 and 8 -2 and 0 2 on the Cartesian plane?
It works out that the circle's centre is at (3, -2) and its radius is 5 on the Cartesian plane.
What is the centre and radius of a circle passing through the points of 5 5 and 8 5 and 5 1 on the Cartesian plane?
Using the formula of x^2 +2gx +y^2 +2fy +c = 0 it works out that the centre of the circle is at (6.5, 3) and its radius is 2.5 units in length. Alternatively plot the points on the Cartesian plane to find the centre and radius of the circle.
What is the Cartesian equation of a circle whose centre is in the 1st quadrant with a radius of 7 and touches the x and y axes?
Centre of the circle is at (7, 7) and its Cartesian equation is (x-7)^2 + (y-7)^2 = 49
What is the centre and area in cm of a circle whose circumference cuts through the points of 1 0 and 7 -6 and 7 0 on the Cartesian plane?
It works out that the centre of the circle is at (4, -3) on the Cartesian plane and its area is 56.549 square cm rounded up to three decimal places.
What is the centre and radius of a circle that passes through the points of 2 0 and 3 1 and -6 10 on the Cartesian plane?
The equation of the circle works out as: (x+2)^2 + (y-5)^2 = 41 The circle's centre is at: (-2, 5) Its radius is the square root of 41
What is the radius of a circle and its centre that passes through the points of 5 0 and 3 4 and -5 0 on the Cartesian plane?
Points: (5, 0) and (3, 4) and (-5, 0) Equation works out as: x^2+y^2 = 25 Radius: 5 units in length Centre of circle is at the point of origin (0, 0) on the Cartesian plane.
What is the equation of a circle that passes through the points of 5 5 and 8 5 and 5 1 on the Cartesian plane showing work?
The points will form a right angle triangle in a circle whose hypotenuse is its diameterLength from (8, 5) to (5, 1) = 5Midpoint: (6.5, 3) which is the centre of the circleRadius: 2.5Equation of the circle: (x-6.5)^2+(y-3)^2 = 6.25
What is the center and radius of a circle whose circumference passes through the points 5 0 and 3 4 and -5 0 on the Cartesian plane?
It has centre (0, 0) and radius 5.
What is the equation of a circle with center (3 8) and a radius of 2?
Centre of the circle: (3, 8) Radius of the circle: 2 Cartesian equation of the circle: (x-3)^2 + (y-8)^2 = 4
What is the centre of a circle called?
The Origin ( or just "origin") * * * * * That is not generally true. The general formula for a circle, in the Cartesian plane, is of the form (x-a)2 + (y-b)2 = r2 where the coordinates of the centre are (a,b) and the radius is r. It is only if both a and b are 0 that the centre is the origin.
What is the distance that passes through the centre of a circle called?
It is the diameter of the circle.
What is a chord that passes through the centre of the circle called?
It is the circle's diameter
