A-LevelMathematicsCoordinate geometry9709/12 · Feb/Mar 2023 · Q56 Marks
Points A (7, 12) and B lie on a circle with centre (–2, 5). The line AB has equation y = −2x + 26. Find the coordinates of B.
- (a)Find the coordinates of B.[6]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.
- [B1] r² = (7+2)²+(12-5)² Expect 130, may use AC rather than r.
- [B1 FT] Equation of circle is (x+2)² +(y−5)² = 130 OE FT their 130, may use distance BC rather than circle.
- [M1] (x+2)²+(-2x+21)² = 130 Substitute y=-2x+26 into a circle equation.
- [M1] 5x²-80x+315 [=0] leading to [5](x−9)(x-7) Factorisation OE must be seen.
- [A1] x=9 With or without x = 7.
- [A1] y = 8 OR (9, 8) y = 8or(9,8) only. Both Al's dependent on the first M1.
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