4. Consider the equation y² - 2x + 6y+ 9 = 0, identify the conic, and find the values o f k such that the family of lines x + 2y + k = 0 satisfies the following condition: a) are tangent to the conic b) Cut the conic at two different points c) Do not cut the conic.

4. Consider the equation y² - 2x + 6y+ 9 = 0, identify the conic, and find the values o f k such that the family of lines x + 2y + k = 0 satisfies the following condition: a) are tangent to the conic b) Cut the conic at two different points c) Do not cut the conic.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 27RE

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Question

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SOLVE STEP BY STEP IN DIGITAL FORMAT
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4. Consider the equation y² - 2x + 6y+ 9 = 0, identify the conic, and find the values o f k such that the family of lines
x + 2y + k = 0 satisfies the following condition:
a) are tangent to the conic
b) Cut the conic at two different points
c) Do not cut the conic.

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Step 1: Given information

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Step 2: Identifying the conic section

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Step 3: Value of 'k' for the family of lines

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Step 4: For a tangent to conic section

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Step 5: b) The line cut the conic at two distinct points

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Step 6: C) The line do not cut the conic section

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