E-TN01 · Two tangents from one point
The curve is \(y=x^2+6\). A tangent touches it at \(T=(a,a^2+6)\).
Show that the tangent at T has equation \(y=2ax+6-a^2\).
Find both tangents from \(P=(0,-3)\), and their points of contact.
Find the distance between the two contact points and the area of the triangle formed by those points and P.
Complete-answer checking, worked solutions and indicative written criteria.
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