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Q.
If the circle $x^{2} + y^{2}-17x + 2fy + c = 0$ passes through $(3,1), (14,-1)$ and $(11,5)$, then $c$ is
Conic Sections
Solution:
Given equation of circle is
$x^{2} + y^{2} - 17x + 2fy + c = 0$.
Since it passes through $(3,1)$, $(14, -1)$ and $(11,5)$
$ \therefore \, 9 + 1 - 51 + 2f+ c = 0$
or $2f+ c = 41$ $\, ...(i)$
and $196 + 1 - 238 - 2f+ c = 0$
or $- 2f+ c = 41$ $\, ...(ii)$
Adding $(i)$ and $(ii)$, we get
$ 2c = \left(2 \times 41\right)$
or $c = 41$.