| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation involving finding the point of tangency |
| Difficulty | Standard +0.3 This is a straightforward multi-part circle question requiring standard techniques: distance formula for diameter, circle equation from centre and radius, and tangent verification via discriminant. While it has multiple parts (7 marks typical), each step follows directly from textbook methods with no problem-solving insight needed. Slightly above average difficulty due to the algebraic manipulation in part (iii), but still routine for C1 level. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
7. A circle has centre $( 5,2 )$ and passes through the point $( 7,3 )$.\\
(i) Find the length of the diameter of the circle.\\
(ii) Find an equation for the circle.\\
(iii) Show that the line $y = 2 x - 3$ is a tangent to the circle and find the coordinates of the point of contact.\\
\hfill \mbox{\textit{OCR C1 Q7 [9]}}