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MathNet 2019-part-06 — 184 problems (EN–VI) Question 118

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 118

Write the equation of the conic on which lie the centres of all those circles that touch both the circle $x^{2}+y^{2}=9$ and the circle $x^{2}+(y-4)^{2}=1$, but do not contain the point $T(0,3)$. Write the equation of the conic in standard form.
(20 points)