Mathematics · 2013
JEE Main · 9 April 2013, Shift 1 · Q65
If each of the lines 5 x+8 y=13 and 4 x-y=3 contains a diameter of the circle x^2+y^2-2(a^2-7 a+11) x-2(a^2-6 a+6) y; +b^3+1=0, then:
If each of the lines $\displaystyle 5 x+8 y=13$ and $\displaystyle 4 x-y=3$ contains a diameter of the circle
$$\begin{aligned}
& x^2+y^2-2\left(a^2-7 a+11\right) x-2\left(a^2-6 a+6\right) y \\
& +b^3+1=0, \text { then : }
\end{aligned}
$$
Official answer
(4)
$\displaystyle a=5 \text { and } b \in(-\infty, 1)$
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JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.