Review question

# Can we show that this point moves on a circle? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6234

## Question

1. The point $A$ has coordinates $(5,16)$ and the point $B$ has coordinates $(-4,4)$. The variable point $P$ has coordinates $(x,y)$ and moves on a path such that $AP = 2BP$. Show that the Cartesian equation of the path of $P$ is $(x + 7)^2 + y^2 = 100.$

2. The point $C$ has coordinates $(a,0)$ and the point $D$ has coordinates $(b,0)$. The variable point $Q$ moves on a path such that $QC = k \times QD,$ where $k > 1$. Given that the path of $Q$ is the same as the path of $P$, show that $\frac{a + 7}{b + 7} = \frac{a^2 + 51}{b^2 + 51}.$ Show further that $(a + 7)(b + 7) = 100$, in the case $a \neq b$.