SECTION 3 (Maximum Marks: 18)
• This section contains SIX questions of matching type.
• This section contains TWO tables (each having 3 columns and 4 rows)
• Based on each table, there are THREE questions.
• Each question has FOUR options
Columns 1, 2 and 3 contain conies, equations of tangents to the conies and points of contact, respectively. | |||
Column 1 | Column 2 | Column 3 | |
(I) | (i) | (P) | |
(II) | (ii) | (Q) | |
(III) | (iii) | (R) | |
(IV) | (iv) | (S) |
is found to be 
, then which of the following options is the only CORRECT combination ? (II)(iv)(R) (ii) If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination ? (I) (ii) (Q) (iii) For 
, if a tangent is drawn to a suitable conic (Column 1) at the point of contact (-1, 1), then which of the following options is the only CORRECT combination for obtaining its equation ? (I)(ii)(Q)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)
Tangent at 
is 
x + 2y = 4
Since slope of tangent at 
is -ve hence possible curve are (I), (II) only
equation of curve is 
+ y 2 = 1, i.e., x 2 + a 2 y 2 = a 2
Hence equation of tangent is y = mx + 
And point of contact is 
(ii)
Tangent at (8, 16) is y = x + 8
Slope of tangent is +ve hence possible curve will be y 2 = 4ax
equation of tangent is my = m 2 x + a and point of contact is
(iii)
For a = 
and point (-1, 1) on the curve is x 2 + y 2 = a 2 equation of tangent is y = mx + a 
and point of contact is 
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