Answer to Question #91539 in Geometry for Sajid

Question

Q. Choose the correct answer.
Q. Which of the following is equation of one of the diameter of the circle , x2+y2+4x-2y=0
a. x+y=0
b. x-y=0
c. 2x-y=0
d. x-2y=0

Answer 1

Solution:

Rewrite the equation: x²+y²+4x-2y=0,

(x²+ 4x + 4) + (y²-2y + 1) – 4 - 1=0,

(x+2)² + (y-1)² -5 = 0,

(x+2)² + (y-1)² = 5. The diameter passes through the centre of the circle, so you should find coordinates of that. Imagine the circle x² + y² = 5 with centre (0,0). The general form of the circle equation is (x+a)² + (y+b)² = c². To get an image of (x+a)² + (y+b)² = 5 you should move the graph for an «a» units to the left in case a > 0, to the right for an «-a» units in case a < 0. Move down the graph for a «b» units in case b > 0 and move up for an «-b» units in case b < 0. In your case a = 2, b = -1. You moved your graph left for a 2 units and for a 1 unit up, so coordinates of your circle are (0-2, 0+1), (-2, 1).

The final stage is to find the equation (from the list) that describes the graph passes through (-2, 1).

Unfortunately, THERE IS NO ANSWER !!! Proof:

a)    x+y =0, -2 + 1 =-1 ≠ 0;       b) x - y =0,     -2 - (1) = - 3 ≠ 0

c)    2x – y = 0,  2*(-2) – (1) = - 5 ≠ 0  d) x - 2y = 0,   -2 – 2*1= - 4 ≠ 0.