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Q.

 COLUMN - I COLUMN - II
A)If p1, p2 be the lengths of perpendiculars 
drawn from the two foci of an ellipse
 x2a2+y2b2=1
to any tangent to it then product of p1. p2 =
p)23
B)The angle between a pair of tangents drawn to the 
ellipse 3x2 + 2y2 = 5 from the point (1, 2) is
q)x – ey – e3a = 0
C)The equation of normal to the ellipsex2a2+y2b2=1
at the positive end of latus rectum is
r)b2
D)If the normal at the point P(θ) to the ellipse 
x214+y25=1meets it again at the point 2θ , then cosθ =
s)tan1125
 (A)(B)(C)(D)
1)pqrs
2)rsqp
3)srpq
4)qspr

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

A) Product of perpendicular from foci to tangent = b
B) tanθ=2abS11x12+y12a2+b2=125
C) Equation of normal at is Laeb2/a is axeay=a2b2 ⇒ xey=ae3
D) Equation of the normal at (P/Q) isaxcosθbysinθ=a2b2 it passes through Q(2θ)
we get cosθ=2/3

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 COLUMN - I COLUMN - IIA)If p1, p2 be the lengths of perpendiculars drawn from the two foci of an ellipse x2a2+y2b2=1to any tangent to it then product of p1. p2 =p)−23B)The angle between a pair of tangents drawn to the ellipse 3x2 + 2y2 = 5 from the point (1, 2) isq)x – ey – e3a = 0C)The equation of normal to the ellipsex2a2+y2b2=1at the positive end of latus rectum isr)b2D)If the normal at the point P(θ) to the ellipse x214+y25=1meets it again at the point 2θ , then cosθ =s)tan−1⁡125 (A)(B)(C)(D)1)pqrs2)rsqp3)srpq4)qspr