Maths-
The line x cos 
+ y sin = p touches the ellipse 
, if :
Maths-General
- none of these
Answer:The correct answer is:
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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 =
maths-
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 -
maths-General
maths-
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
maths-General
physics-
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
physics-General
physics-
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
physics-
The Maxwell's four equations are written as:
i) 
ii) 
iii) 
iv) 
The equations which have sources of 
and 
The Maxwell's four equations are written as:
i)
ii)
iii)
iv)
The equations which have sources of and
physics-General
maths-
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 –
maths-General
maths-
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 =
maths-General
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
=
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)
maths-
If P(), Q 
are points on ellipse and is angle between normals at P and Q then -
If P(), Q are points on ellipse and is angle between normals at P and Q then -
maths-General
maths-
If 
are the eccentric angles of the extremities of a focal chord of the ellipse 
, then tan 
The equation of the ellipse is of the form 
the eccentricity e = 
=
.
Let P(4 cos, 3 sin ) and Q (4 cos , 3 sin ) be a focal chord of the ellipse passing through the focus at (
, 0).
Then
=
=
=
tan 
tan 
= 
= 
.
the eccentricity e = =.Let P(4 cos
, 3 sin ) and Q (4 cos , 3 sin ) be a focal chord of the ellipse passing through the focus at (, 0).Then
== = tan tan = = .If are the eccentric angles of the extremities of a focal chord of the ellipse , then tan
maths-General
The equation of the ellipse is of the form
the eccentricity e = =.
Let P(4 cos, 3 sin ) and Q (4 cos , 3 sin ) be a focal chord of the ellipse passing through the focus at (, 0).
Then=
=
=
tan tan = = .
the eccentricity e = =.Let P(4 cos
, 3 sin ) and Q (4 cos , 3 sin ) be a focal chord of the ellipse passing through the focus at (, 0).Then
== = tan tan = = .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
tan = cot2 maths-
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
=
= 
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 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
=
= physics-
The sun deliverse 
of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions 8m ,20m, will be:
The sun deliverse of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions 8m ,20m, will be:
physics-General