Find the equations of the tangent to the curve $y=x^2$ at the point $(t, t^2)$, expressing the c

Question

Find the equations of the tangent to the curve $y=x^2$ at the point $(t, t^2)$, expressing the coefficients in terms of $t$ where necessary.[3] Find the equations of all lines that are tangents to both the curves $y=x^2$ and $y=-x^2+8x-16$.[4]

Accepted Answer

(i) $y=2tx-t^2$ (ii) $y=0$ and $y=8x-16$

NJC IP4 Tangents and Normals Tutorial Q3

NJC IP4 Tangents and Normals Tutorial Q3

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