the straight line 2x-y+8=0 and the circle 2x^2+2y^2-3x+2y+k=0 do not have any intersection points,where k is a constant.find the range of the values of k

Question

the straight line 2x-y+8=0 and the circle 2x^2+2y^2-3x+2y+k=0 do not have any intersection points,where k is a constant.find the range of the values of k
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Solution 1

Step 1: Rewrite the equation of the line in slope-intercept form (y = mx + b). The equation 2x - y + 8 = 0 can be rewritten as y = 2x + 8.

Step 2: Substitute y = 2x + 8 into the equation of the circle. This gives us 2x^2 + 2(2x + 8)^2 - 3x + 2(2x + 8) + k = 0.

Step 3: Simplify the equation. This g Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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