jee-main 2021 Q64

jee-main · India · session3_22jul_shift1 Circles Circle-Line Intersection and Point Conditions

Let the circle $S : 36 x ^ { 2 } + 36 y ^ { 2 } - 108 x + 120 y + C = 0$ be such that it neither intersects nor touches the coordinate axes. If the point of intersection of the lines, $x - 2 y = 4$ and $2 x - y = 5$ lies inside the circle $S$, then:
(1) $\frac { 25 } { 9 } < C < \frac { 13 } { 3 }$
(2) $100 < C < 165$
(3) $81 < C < 156$
(4) $100 < C < 156$

Let the circle $S : 36 x ^ { 2 } + 36 y ^ { 2 } - 108 x + 120 y + C = 0$ be such that it neither intersects nor touches the coordinate axes. If the point of intersection of the lines, $x - 2 y = 4$ and $2 x - y = 5$ lies inside the circle $S$, then:\\
(1) $\frac { 25 } { 9 } < C < \frac { 13 } { 3 }$\\
(2) $100 < C < 165$\\
(3) $81 < C < 156$\\
(4) $100 < C < 156$

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