What is the tangent line to the curve at the given point?

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SUMMARY

The tangent line to the curve defined by the equation y²(y² - 4) = x²(x² - 5) at the point (0, -2) is confirmed to be y = -2. The derivative dy/dx was calculated, resulting in a slope of 0, indicating a horizontal tangent line at the specified point. This conclusion is validated by the discussion participants, affirming the correctness of the solution.

PREREQUISITES
  • Understanding of implicit differentiation
  • Familiarity with the concept of tangent lines in calculus
  • Knowledge of the equation of a line in slope-intercept form
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study implicit differentiation techniques in calculus
  • Explore the properties of tangent lines and their applications
  • Learn how to find derivatives of complex equations
  • Review slope-intercept form and its significance in graphing
USEFUL FOR

Students studying calculus, particularly those focusing on derivatives and tangent lines, as well as educators seeking to reinforce these concepts in their teaching materials.

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Homework Statement


Find the tangent line to the curve y^2 (y^2 - 4) = x^2 (x^2 -5) at the point (0,-2).


Homework Equations


y-y1=m(x-x1)


The Attempt at a Solution


I d/dx-ed both sides and was left with dy/dx=0
so
y=-2
Does that seem right?
 
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Yup that's correct!
 

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