The equation of an ellipse is 2x² + 6y² + 6x-8y-6 = 0; determines the values of parameter k for which the lines of the family 5x + 2y + k = 0: a) They cut the ellipse at two different points b) They are tangent to the ellipse c) They do not intersect the ellipse ***

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE
The equation of an ellipse is 2x² + 6y² + 6x - 8y-6 = 0;
determines the values of parameter k for which the lines of the family 5x + 2y + k = 0:
a) They cut the ellipse at two different points
b) They are tangent to the ellipse
c) They do not intersect the ellipse
***
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE The equation of an ellipse is 2x² + 6y² + 6x - 8y-6 = 0; determines the values of parameter k for which the lines of the family 5x + 2y + k = 0: a) They cut the ellipse at two different points b) They are tangent to the ellipse c) They do not intersect the ellipse ***
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Step 1

For a quadratic equation of the form: ax2+bx+c=0, the discriminant: is calculated using the equation: D=b2-4ac.

  • If D>0, then the quadric equation has two real and unequal roots.
  • If D=0, then the roots are real and equal.
  • If D<0, the roots are imaginary and unequal.
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