Moderate -0.3 This is a straightforward substitution problem requiring students to substitute the linear equation into the conic, solve the resulting quadratic, and find coordinates. While it involves a hyperbola rather than a circle, the method is standard and requires no novel insight—slightly easier than average due to being a direct application of a well-practiced technique with clean arithmetic.
8 In this question you must show detailed reasoning.
Determine the coordinates of the point of intersection of the line with equation \(y = 2 x + 3\) and the curve with equation \(y ^ { 2 } - 4 x ^ { 2 } = 33\).
Expansion of the quadratic to obtain a correct equation, allow one sign error or one coefficient error, this can be implied by a correct linear equation.
Expansion of the quadratic to obtain a correct equation, allow one sign error or one coefficient error, this can be implied by a correct linear equation.
\(y = 7\)
A1
Progress to solve and obtain correct value
\((2, 7)\) cao
A1
## Question 8:
| Answer | Mark | Guidance |
|--------|------|----------|
| $(2x+3)^2 - 4x^2 = 33$ | B1 | substitution to eliminate $y$ |
| $4x^2 + 12x + 9 - 4x^2 = 33$ or $12x + 9 = 33$ | M1 | Expansion of the quadratic to obtain a **correct equation, allow one sign error or one coefficient error**, this can be implied by a correct linear equation. |
| $x = 2$ | A1 | Progress to solve and obtain correct value |
| $(2, 7)$ cao | A1 | |
| **Alternative:** $y^2 - 4\left(\frac{y-3}{2}\right)^2 = 33$ | B1 | substitution to eliminate $x$ |
| $y^2 - (y^2 - 6y + 9) = 33$ or $6y - 9 = 33$ | M1 | Expansion of the quadratic to obtain a **correct equation**, allow **one sign error or one coefficient error**, this can be implied by a correct linear equation. |
| $y = 7$ | A1 | Progress to solve and obtain correct value |
| $(2, 7)$ cao | A1 | |
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8 In this question you must show detailed reasoning.
Determine the coordinates of the point of intersection of the line with equation $y = 2 x + 3$ and the curve with equation $y ^ { 2 } - 4 x ^ { 2 } = 33$.
\hfill \mbox{\textit{OCR MEI AS Paper 2 2024 Q8 [4]}}