x^2-6x+y^2=-5

Question

Sketch the graph of the equation.  How?

Answer 1

Given equation is x^2-6x+y^2 = -5

Add 9 to each side.

x^2-6x+y^2+9 = -5+9

x^2-6x+9+y^2 = 4

(x-3)^2+(y-0)^2 = r^2

Compare it standard circle equation is (x-h)^2+(y-k)^2 = r^2

(h,k) = (3,0)

radius is 2.

Graph

Draw the coordinate plane.

Plot the center point of circle.

Draw the circle use radius is 2units and  the center point.

 

Answer 2

The equation x ² - 6x + y ² = -5

To change the expression into a perfect square  add (half the x coefficient)² to each side of the expression.

Here x coefficient = -6. so, (half the x coefficient)² = (-6/2)²= 9

Add 9 to each side.

x ² - 6x  + 9 + y ² = -5 + 9

(x - 3)² + (y - 0)² = 2²

Compare it to standard form of a circle equation is

Where center is (h ,k ) and radius of circle is r .

Center of circle is (3,0) and radius is 2.

To graph the circle we need few more coordinates.

Center at (3,0) and r = 2, So we plot

Up (3, 0+2) = (3, 2)

Down (3, 0-2) = (3, -2)

Left (3-2, 0) = (1, 0)

Right (3+2, 0) = (5, 0)

Graph

1. draw the coordinate plane.

2. Plot the center at (3,0).

3. Plot 4 points " radius" away from the center in the up, down, left and right direction.

4. Sketch the circle.