If the tangent at the point $P$ on the circle ${x^2} + {y^2} + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the $y$- axis, then the length of $PQ$ is
If the tangent at the point $P$ on the circle ${x^2} + {y^2} + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the $y$- axis, then the length of $PQ$ is
- [IIT 2002]
- A
$4$
- B
$2\sqrt 5 $
- C
$5$
- D
$3\sqrt 5 $
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- [JEE MAIN 2023]
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$
Column $II$
$(A)$ Two intersecting circles
$(p)$ have a common tangent
$(B)$ Two mutually external circles
$(q)$ have a common normal
$(C)$ two circles, one strictly inside the other
$(r)$ do not have a common tangent
$(D)$ two branches of a hyperbola
$(s)$ do not have a common normal
Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ Two intersecting circles | $(p)$ have a common tangent |
| $(B)$ Two mutually external circles | $(q)$ have a common normal |
| $(C)$ two circles, one strictly inside the other | $(r)$ do not have a common tangent |
| $(D)$ two branches of a hyperbola | $(s)$ do not have a common normal |
- [IIT 2007]