TMUA Sed (CoderLovesEggs) Paper 1 with Solutions · Question 11

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Sed (CoderLovesEggs) Paper 1 with Solutions · Q11

Paper 1Geometry

Let $T=(4,6)$ be a point on the circle

C:(x-3)^2+(y-4)^2=5.

Let $P=(p,q)$ . The circle centred at $P$ passing through $T$ has area $\pi(p^2+q^2)$ and is tangent to $C$ at $T$ .

It follows that $P$ is:

(2,3)

;

\left(\dfrac{41}{22},\dfrac{19}{11}\right)

;

\left(\dfrac{17}4,\dfrac32\right)

;

\left(-\dfrac78,-\dfrac{15}4\right)

;

\left(\dfrac{19}8,\dfrac{11}4\right)

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