Find Points of Tangency: 9x^2 - y^2 =36

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The discussion focuses on finding the points of tangency for the hyperbola defined by the equation 9x² - y² = 36. The user employs implicit differentiation, resulting in the derivative y' = 9x/y. To determine the points of tangency, the user seeks clarification on whether to substitute specific x and y values into the derived equation. The conversation emphasizes the importance of correctly applying implicit differentiation to identify tangent lines that intersect the y-axis.

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I have the following function given, and I need to find the points of tangency...
Two tangent lines to the huperbola 9x^2 - y^2 =36 interesect at the y-axis.

Use implicit differentiation to find the points of tangency.

Ok so i multiplied both sides by dy/dx, and solved for y'...i got
y'= \frac {9x}{y}
so to find the points of tangency, do i plug in the x and y values? I am a little confused on that...thanks.
 
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