SPS SPS FM 2024 October — Question 7

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionOctober
TopicDifferentiation Applications
TypeFind normal line equation

7. The diagram shows part of the graph of \(y = x ^ { 2 }\). The normal to the curve at the point \(A ( 1,1 )\) meets the curve again at \(B\). Angle \(A O B\) is denoted by \(\alpha\).
\includegraphics[max width=\textwidth, alt={}, center]{1e5d102a-955d-4968-8328-339f12665e01-16_506_741_283_217}
  1. Determine the coordinates of \(B\).
  2. Hence determine the exact value of \(\tan \alpha\).
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