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JEE Advanced 2020 Concept Recapitulation Test 4 Paper 2

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Answer the following by appropriately matchingthe list based on the information given in the paragraph.
Consider the following equations of curves:
C1:x2+y2=4C_{1}: x^{2}+y^{2}=4
C2:y2=8√6xC_{2}: y^{2}=8 √{6} x
C3:  x2/1+  y2/5=1C_{3}: \;{x^{2}}/{1}+\;{y^{2}}/{5}=1
C4:  x2/25−  y2/1=1C_{4}: \;{x^{2}}/{25}-\;{y^{2}}/{1}=1
List-l: Contains the equation of common tangent between two of the given curves
List-Il: Contains some information
 List - I  List - II
 (I) y=√2(x+√6)y=√{2}(x+√{6})  (P) Is a chord of C1C_{1}
 (II) y=√3x+2√2y=√{3} x+2 √{2}  (Q) Is not a chord of C4C_{4}
 (III) y=  1/√3x+  4/√3y=\;{1}/{√{3}} x+\;{4}/{√{3}}  (R) Common tangent of C1&C3C_{1} \& C_{3}
 (IV) y=x+2√6y=x+2 √{6}  (S) Common tangent of C2&C4C_{2} \& C_{4}
   (T) Common tangent of C1&C2C_{1} \& C_{2}
   (U) Common tangent of C2&C3C_{2} \& C_{3}
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