Maths-
General
Easy
Question
The line x cos 
+ y sin = p touches the ellipse 
, if :
- none of these
Hint:
In this question, we have to find the correct option if the line x cos + y sin = p touches the ellipse . For this we will first have to solve the given equation to find the value of 
and later substitute in the equation of ellipse to find the correct equation.
The correct answer is:
Related Questions to study
maths-
If and 
are the eccentric angles of extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
Equation of chord be
cos 
+ 
sin = cos
since it passes through (ae, 0)
so e cos = cos
e =
= 
e =
cos + sin = cossince it passes through (ae, 0)
so e cos
= cose =
= e =
If and are the eccentric angles of extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
maths-General
Equation of chord be
cos + sin = cos
since it passes through (ae, 0)
so e cos = cos
e = =
e =
cos + sin = cossince it passes through (ae, 0)
so e cos
= cose =
= e =
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If x cos + y sin = p is a tangent to the ellipse , then -
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
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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
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physics-General
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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
physics-General
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If P (a cos
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If P (a cos, bsin) is a point on an ellipse , then ' ' is –
maths-General
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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 =
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maths-
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)
+= 1Slope 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-
maths-General
Let tangent is += 1
Slope is tan = – S… (1)
square of length of intercept is
=
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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,
the path difference produced is 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
physics-General
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,
the path difference produced is 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 = cot2 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 -
maths-General
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
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The radius of the circle passing through the points of intersection of ellipse 
= 1 and x2 – y2 = 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
=
= 
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= 0 and = 1, we get = Therefore radius of circle
=
= The radius of the circle passing through the points of intersection of ellipse = 1 and x2 – y2 = 0 is -
maths-General
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
=
= maths-
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 =
= 
= If are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is -
maths-General
are collinear. 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 aretan and
tan
tan = 
=
=
sin cos = 
sin 2
The greatest value of tan = .1 = .
, b sin ) Equation of the diameter CP is y =
xThe normal to ellipse at P is
ax sec
– by cosec = a2e2Slopes 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–
maths-General
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 aretan andtan
tan = =
=sin cos = sin 2
The greatest value of tan = .1 = .
, b sin ) Equation of the diameter CP is y =
xThe normal to ellipse at P is
ax sec
– by cosec = a2e2Slopes 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
physics-General
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 PA2 + PB2 = 10 where A = (2, 0) and B = (4, 0) is
The locus of P such that PA2 + PB2 = 10 where A = (2, 0) and B = (4, 0) is
Maths-General
