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Application Q4
Developed by Dept. of Math., Malda College
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The envelope of the parabola√((x/a))+√((y/b))=1 , where ab=c², c is a fixed constant, a and b being variable parameter, is
xy = c²
4xy = c²
16xy = c²
3xy = c²
Clear selection
Number of envelopes of the family of circles (x-α)²+y²=4 is ( α parameter )
2
1
0
4
Clear selection
The envelope of the family of straight lines y=mx+(5/m)(m is parameter) is
y²=10x
y²=x
y²=20x
y = x
Clear selection
The envelope of the family of parabolas x²=4ay, a is a parameter, is
x = 0
y = 0
y = 1
x = 5
Clear selection
An envelope of the family of circles (x-α)²+y²=4 is ( α parameter ) is
x = 2
y = 0
y = -2
x = 5
Other:
Clear selection
The envelope of the system of the parabolas ax²+a²y=1, a being the parameter, is
x⁴+4y=0
x²-4y²=0
x²-4y=0
x³+4y=0
Clear selection
If Aα²+Bα+C=0 is family of straight lines where A, B, C are linear functions of x, y and α is a parameter then the envelope of this family is given by
B=(A/C)
B²-AC=0
C²-AB=0
B²-4AC=0
Clear selection
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