Application Q4

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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 )

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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