graphing this circle equation: x^2+y^2-14x+4y=0

Question

i need help finding the solution of this conic . please help

Answer 1

Given equation x^2+y^2-14x+4y = 0

Compare x^2+y^2+2gx+2fy+c = 0

2g = -14 , 2f = 4,   c = 0

g = -7        f = 2

(h,k) = (-g,-f) = (7,-2)

radius = sqrt(g^2+f^2-c) = sqrt(49+4-0) = sqrt(53) = 7.2

Answer 2

The standard form of the circle equation is ( x - h )² + ( y - k )² = r², where, (h, k) is the center of the circle, and r is the radius.

The equation is x² + y² - 14x + 4y = 0.

Write the equation in standard form of a circle.

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

Here, x coefficient = - 14, so, (half the x coefficient)² = (- 14/2)²= 49.

Here y coefficient = 4, so, (half the y coefficient)² = (4/2)²= 4.

Add 49 and 4 to each side.

x² - 14x + 49 + y² + 4y + 4 = 0 + 49 + 4

(x - 7)² + (y + 2)² =53

(x - 7)² + (y - (- 2))² = (√53)².

Compare the equation with standard form of a circle equation.

The center (h, k) is (7, - 2), and the radius (r) is √53 = 7.28 units.

GRAPH :

1. Draw the coordinate plane.

2. Place the center of the circle at (7, - 2).

3. Plot the radius points on the coordinate plane.

   Since the radius is 7.28 units,

  Count 7.28 units up, down, left, and right from the center (7, - 2).

  This means that,

  Up (7, - 2 + 7.28) = (7, 5.28)

  Down (7, - 2 - 7.28) = (7, - 9.28)

  Left (7 - 7.28, - 2) = (- 0.28, - 2)

  Right (7 + 7.28, - 2) = (14.28, - 2)

  The circle should has the points at (7, 5.28), (7, - 9.28), (- 0.28, - 2), and (14.28, - 2).

4. Connect the plotted points to the graph of the circle with a round, smooth  curve.