Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
← IIT-JEE 2007 · Paper 2
MathematicsMatrix match+6Question 66 of 66
IIT-JEE 2007 · Paper 2, Mathematics question 66
Column I
- ATwo intersecting circles
- BTwo mutually external circles
- CTwo circles, one strictly inside the other
- DTwo branches of a hyperbola
Column II
- Phave a common tangent
- Qhave a common normal
- Rdo not have a common tangent
- Sdo not have a common normal
| P | Q | R | S | |
|---|---|---|---|---|
| A | ||||
| B | ||||
| C | ||||
| D |
Answer and worked solution
Official answer: A → P, Q; B → P, Q; C → Q, R; D → Q, R
Common normal. For two circles the line of centres is normal to both; for a hyperbola the transverse axis is normal to both branches. So every item has Q.
- A, intersecting circles: two common (direct) tangents. → P, Q.
- B, external circles: four common tangents. → P, Q.
- C, one circle strictly inside the other: any tangent to the inner circle cuts the outer one, so there is no common tangent. → Q, R.
- D, two branches of a hyperbola: a tangent to one branch never touches the other (the asymptotes are limits, not tangents), so there is no common tangent. → Q, R.
Answer: A → P, Q; B → P, Q; C → Q, R; D → Q, R