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If x cos + y sin = p is a tangent to the ellipse , then 



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Equation of chord of the ellipse joining the points P (a cos, b sin ) and Q (a cos , b sin ) is 7
Equation of chord of the ellipse joining the points P (a cos, b sin ) and Q (a cos , b sin ) is 7
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In Young's double slit experiment, 12 fringes are obtained to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by
In Young's double slit experiment, 12 fringes are obtained to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by
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Intensity of central bright fringe due to interference of two identical coherent monochromatic sources is I. If one of the source is switched off, then intensity of central bright fringe becomes
Intensity of central bright fringe due to interference of two identical coherent monochromatic sources is I. If one of the source is switched off, then intensity of central bright fringe becomes
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If P (a cos, bsin) is a point on an ellipse , then ' ' is –
If P (a cos, bsin) is a point on an ellipse , then ' ' is –
mathsGeneral
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If the normal at the point P() to the ellipse intersects it again at the point Q(2) then cos =
If the normal at the point P() to the ellipse intersects it again at the point Q(2) then cos =
mathsGeneral
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If a tangent to ellipse + = 1 makes an angle with x axis, then square of length of intercept of tangent cut between axes is
Let tangent is += 1
Slope is tan = – S… (1)
square of length of intercept is
=
Length is … (2)
Now use value of tan from (1)
Slope is tan = – S… (1)
square of length of intercept is
=
Length is … (2)
Now use value of tan from (1)
If a tangent to ellipse + = 1 makes an angle with x axis, then square of length of intercept of tangent cut between axes is
mathsGeneral
Let tangent is += 1
Slope is tan = – S… (1)
square of length of intercept is
=
Length is … (2)
Now use value of tan from (1)
Slope is tan = – S… (1)
square of length of intercept is
=
Length is … (2)
Now use value of tan from (1)
physics
Vibrating tuning fork of frequency is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through the intensity of sound changes from a maximum to minimum. If the speed of sound is then is
When the piston is moved through a distance of the path difference produced is
This must be equal to for maximum to change to minimum.
So,
This must be equal to for maximum to change to minimum.
So,
Vibrating tuning fork of frequency is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through the intensity of sound changes from a maximum to minimum. If the speed of sound is then is
physicsGeneral
When the piston is moved through a distance of the path difference produced is
This must be equal to for maximum to change to minimum.
So,
This must be equal to for maximum to change to minimum.
So,
maths
PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R and
, respectively then tan tan is equal to 
P (a cos 2 , b sin 2 ), Q (a cos 2 , b sin 2 )
R (a cos 2 , b sin 2 )
chord's PQ equation
cos ( + ) + sin ( + ) = cos ( – )
PQ passes through the focus (ae, 0)
e =
PR passes through the focus (– ae, 0) the
– e =
= –
Apply componendo and dividendo, we get
=
=
tan tan = cot^{2}
PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R and
, respectively then tan tan is equal to 
mathsGeneral
P (a cos 2 , b sin 2 ), Q (a cos 2 , b sin 2 )
R (a cos 2 , b sin 2 )
chord's PQ equation
cos ( + ) + sin ( + ) = cos ( – )
PQ passes through the focus (ae, 0)
e =
PR passes through the focus (– ae, 0) the
– e =
= –
Apply componendo and dividendo, we get
=
=
tan tan = cot^{2}
maths
The radius of the circle passing through the points of intersection of ellipse = 1 and x^{2 }– y^{2} = 0 is 
Two curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin.
Solving = 0 and = 1, we get
=
Therefore radius of circle
= =
Solving = 0 and = 1, we get
=
Therefore radius of circle
= =
The radius of the circle passing through the points of intersection of ellipse = 1 and x^{2 }– y^{2} = 0 is 
mathsGeneral
Two curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin.
Solving = 0 and = 1, we get
=
Therefore radius of circle
= =
Solving = 0 and = 1, we get
=
Therefore radius of circle
= =
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If are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is 
are collinear.
e = = =
e = = =
If are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is 
mathsGeneral
are collinear.
e = = =
e = = =
maths
If is the angle between the diameter through any point on a standard ellipse and the normal at the point, then the greatest value of tan is–
Any point P on ellipse is (a cos , b sin )
Equation of the diameter CP is y = x
The normal to ellipse at P is
ax sec – by cosec = a2e2
Slopes of the lines CP and the normal GP are tan andtan
tan = =
=sin cos = sin 2
The greatest value of tan = .1 = .
Equation of the diameter CP is y = x
The normal to ellipse at P is
ax sec – by cosec = a2e2
Slopes of the lines CP and the normal GP are tan andtan
tan = =
=sin cos = sin 2
The greatest value of tan = .1 = .
If is the angle between the diameter through any point on a standard ellipse and the normal at the point, then the greatest value of tan is–
mathsGeneral
Any point P on ellipse is (a cos , b sin )
Equation of the diameter CP is y = x
The normal to ellipse at P is
ax sec – by cosec = a2e2
Slopes of the lines CP and the normal GP are tan andtan
tan = =
=sin cos = sin 2
The greatest value of tan = .1 = .
Equation of the diameter CP is y = x
The normal to ellipse at P is
ax sec – by cosec = a2e2
Slopes of the lines CP and the normal GP are tan andtan
tan = =
=sin cos = sin 2
The greatest value of tan = .1 = .
physics
A radar operates at wavelength 50.0 cm. If the beat freqency between the transmitted singal and the singal reflected from aircraft ( ) is 1 kHz, then velocity of the aircraft will be
when source is fixed and observer is moving towards it
when source is moving towards observer at rest
= 900 km/hr
when source is moving towards observer at rest
= 900 km/hr
A radar operates at wavelength 50.0 cm. If the beat freqency between the transmitted singal and the singal reflected from aircraft ( ) is 1 kHz, then velocity of the aircraft will be
physicsGeneral
when source is fixed and observer is moving towards it
when source is moving towards observer at rest
= 900 km/hr
when source is moving towards observer at rest
= 900 km/hr
maths
The locus of P such that PA^{2} + PB^{2} = 10 where A = (2, 0) and B = (4, 0) is
The locus of P such that PA^{2} + PB^{2} = 10 where A = (2, 0) and B = (4, 0) is
mathsGeneral
maths
Let L = 0 is a tangent to ellipse + = 1 and S, be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from on L = 0 is
Let L = 0 is a tangent to ellipse + = 1 and S, be its foci. If length of perpendicular from S on L = 0 is 2 then length of perpendicular from on L = 0 is
mathsGeneral
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The condition that the line x + my = n may be a normal to the ellipse + = 1 is
The condition that the line x + my = n may be a normal to the ellipse + = 1 is
mathsGeneral