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10.1 circle and system of circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.1 circle and system of circle1 Mark
MCQ
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
  • ✓
    $A \rightarrow q, s ; B \rightarrow p, s ; C \rightarrow q, p ; D \rightarrow q, p$
  • B
    $A \rightarrow s, r ; B \rightarrow p, s ; C \rightarrow r, r ; D \rightarrow p, s$
  • C
    $A \rightarrow s, r ; B \rightarrow s, r ; C \rightarrow s, r ; D \rightarrow r, s$
  • D
    $A \rightarrow p, q ; B \rightarrow p, q ; C \rightarrow q, r ; D \rightarrow q, r$
✓

Answer

Correct option: A.
$A \rightarrow q, s ; B \rightarrow p, s ; C \rightarrow q, p ; D \rightarrow q, p$
a
$(A)$ When two circles are intersecting they have a common normal and common tangent.

$(B)$ Two mutually external circles have a common normal and common tangent.

$(C)$ When one circle lies inside of other then, they have a common normal but no common tangent.

$(D)$ Two branches of a hyperbola have a common normal but no common tangent.

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