2.8: Substituting a surd into a curve equation

0606/22/M/J/20 — Question 2 · 5 marks

Do not use a calculator in this question.

(a)
The point (1−5,p)(1 - \sqrt{5}, p) lies on the curve y=10+25x2y = \dfrac{10 + 2\sqrt{5}}{x^{2}}. Find the exact value of pp, simplifying your answer.
[5]