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Find the equations of

**all**lines tangent to [tex] y = x^2 - 4 [/tex] that pass through the point [tex] P(5,5) [/tex]

My solution:

If [tex] f(x) = x^2 - 4 [/tex] then [tex] f'(x) = 2x [/tex]. So

[tex] y - 5 = 10(x-5) [/tex]

This is just tthe equation of 1 tangent line. To find all tangent lines would I have to add some constant

**c**to the equation?

Thanks a lot