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Question 10 College Algebra. Please help

Question 10 College Algebra. Please help-example-1
User Alan John
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1 Answer

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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

User Kiran Jadhav
by
7.6k points

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