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Question

Given below are Matching Type Questions, with two columns(each having some items) each.Each item of column I has to be matched with the items of column II, by encircling the correct matches:Note:An item of Column I can be matched with more than one items in Column II.All the items of Column II have to be matched.

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Solution

(A)25(x2+y2)=(4x+3y12)2
or 25x2+25y2=16x2+9y2+24xy96x72y+144
9x2+16y224xy=96x72y+144
(3x4y)2=24(4x+3y6)
25×(3x4y5)2=24(4x+3y65)×5
(3x4y5)2=245(4x+3y65)
Let 3x4y5=Y and 4x+3y65=X
Y2=245X
On comparing with Y2=4ρX
4ρ=245ρ=65
Equation of directrix is Xρ=0
4x+3y6565=0
or 4x+3y=12
(B)
25(x2+y2)=(4x3y+12)2
or 25x2+25y2=16x2+9y224xy+96x72y+144
9x2+16y2+24xy=96x72y+144
(3x+4y)2=24(4x+3y+6)
25×(3x+4y5)2=24(4x3y+65)×5
(3x+4y5)2=245(4x3y+65)
Let 3x+4y5=Y and 4x3y+65=X
Y2=245X
On comparing with Y2=4ρX
4ρ=245ρ=65
Equation of directrix is X+ρ=0
4x3y+65+65=0
or 4x3y+12=0
and axis of the parabola is Y=0
3x+4y5=0
or 3x+4y=0
(C)
25(x2+y2)=(3x4y+12)2
or 25x2+25y2=9x2+16y224xy+72x96y+144
16x2+9y2+24xy=72x96y+144
25×(4x+3y5)2=24(3x4y+65)×5
(4x+3y5)2=245(3x4y+65)
Let 4x+3y5=Y and 3x4y+65=X
Y2=245X
On comparing with Y2=4ρX
4ρ=245ρ=65
Equation of directrix is X+ρ=0
3x4y+65+65=0
or 3x4y+12=0
and axis of the parabola is
Y=0
or 4x+3y=0

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