Pearson Edexcel IAL Mathematics P2.3.1 Coordinate geometry of the circle

M1: Attempts radius or radius ${ }^{2}$. Condone slips on lhs, for example r or $d=(\text { " } 9 \text { " }-4)^{2}+(\text { " }-5 \text { " }+3)^{2}$ You must see an attempt to take the difference for both components before each are squared.

M1: Correct form of equation E.g. $(x-4)^{2}+(y+3)^{2}=" r "{ }^{2}$
Look for $(x-4)^{2}+(y+3)^{2}=(\text { " } 9 \text { " }-4)^{2}+(\text { " }-5 \text { " }+3)^{2}$
Condone for this mark a slip on one of the components when finding their $r^{2}$
A1: $(x-4)^{2}+(y+3)^{2}=29$ or exact equivalent. The constant terms must be collected and not 25+4 ISW after a correct answer.

Alt (b)(ii)
Note that an alternative version is $x^{2}+y^{2}-8 x+6 y-4=0$. It is possible to proceed using this alternative version of the formula for a circle

M1: States equation of circle is $x^{2}+y^{2}-8 x+6 y+c=0$
M1: Substitutes their N=(9,-5) into $x^{2}+y^{2}-8 x+6 y+c=0$ o.e. and finds " c "

A1: $x^{2}+y^{2}-8 x+6 y-4=0$ o.e.