Challenging +1.2 This question requires finding a general tangent equation, setting up equations for two tangents with x-coordinates differing by 5, solving for their intersection point, and eliminating the parameter to find the locus. While it involves multiple steps and algebraic manipulation beyond routine differentiation, the techniques are standard A-level methods (differentiation, simultaneous equations, parametric elimination) with clear structure provided by the problem setup.
18 A student is investigating the intersection points of tangents to the curve \(y = 6 x ^ { 2 } - 7 x + 1\). She uses software to draw tangents at pairs of points with \(x\)-coordinates differing by 5 .
Find the equation of the curve that all the intersection points lie on.
Substitute \(a = 6\) and \(h = 5\) into formula from line 19 of article
M1
Correct answer
A1
Allow 2 marks for a completely correct valid alternative method
## Question 18:
| Working/Answer | Marks | Guidance |
|---|---|---|
| Substitute $a = 6$ and $h = 5$ into formula from line 19 of article | M1 | |
| Correct answer | A1 | Allow 2 marks for a completely correct valid alternative method |
18 A student is investigating the intersection points of tangents to the curve $y = 6 x ^ { 2 } - 7 x + 1$. She uses software to draw tangents at pairs of points with $x$-coordinates differing by 5 .
Find the equation of the curve that all the intersection points lie on.
\hfill \mbox{\textit{OCR MEI Paper 3 2024 Q18 [2]}}