The value of k that makes the graph of the equation a single point is k = 26
How to determine the value of k
From the question, we have the following parameters that can be used in our computation:
2x² + 2y² + 8x - 12y + k = 0
To determine the value of k, we rewrite the equation by completing the squares for both x² and y² terms.
So, we have
2x² + 8x + 2y² - 12y = -k
Divide both sides by 2
x² + 4x + y² - 6y = -k/2
So, we have
(x + 2)² + (y - 3)² = -k/2 + 4 + 9
(x + 2)² + (y - 3)² = -k/2 + 13
For the equation to represent a single point, we need -k/2 + 13 = 0.
Solving for k, we get:
k/2 = 13
k = 26
Hence, the value of k that makes the graph of the equation a single point is k = 26