Question
S1: The differential equation of parabolas having their vertices at the origin and foci on the x-axis is an equation whose variables are separable
S2: The differential equation of the straight lines which are at a fixed distance p from the origin is an equation of degree 2
S3: The differential equation of all conics whose both axes coincide with the axes of coordinates is an equation of order 2
S2: The differential equation of the straight lines which are at a fixed distance p from the origin is an equation of degree 2
S3: The differential equation of all conics whose both axes coincide with the axes of coordinates is an equation of order 2
Answer: Option A
:
A
S1 -Equation of parabola is y2=±4ax
2ydydx=±ra
D.E of parabola ⇒y2=2yxdydx
2dyy=dxx
Which is variable seperable
S2 -Equation of line which is fixed distance. P from origin can be equation of tangent to circle
s2+y2=p2
Line is y=mx+p√1+m2(m=dydx)
(y−xdydx)2=P(1+(dydx)2)
So, degree is 2
S3 -Equation of conic whose both axis co-incide with co-ordinate axis is ax2+by2=1
As there are two constants, so order of D.E is 2
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:
A
S1 -Equation of parabola is y2=±4ax
2ydydx=±ra
D.E of parabola ⇒y2=2yxdydx
2dyy=dxx
Which is variable seperable
S2 -Equation of line which is fixed distance. P from origin can be equation of tangent to circle
s2+y2=p2
Line is y=mx+p√1+m2(m=dydx)
(y−xdydx)2=P(1+(dydx)2)
So, degree is 2
S3 -Equation of conic whose both axis co-incide with co-ordinate axis is ax2+by2=1
As there are two constants, so order of D.E is 2
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