Maths-
General
Easy
Question
The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is
- a1/3x + b1/3y + (ab) = 0
- a1/3x + b1/3y + (ab)2/3 = 0
- b1/3x + a1/3y + (ab)1/3 = 0
- b1/3x – a1/3y – (ab)1/3 = 0
The correct answer is: a1/3x + b1/3y + (ab)2/3 = 0
Tangent of parabola y2 = 4ax is y = mx + a/m, which also touches to the parabola x2 = 4by 
a/m = – bm2m = –(a/b)1/3
Related Questions to study
maths-
A line L passing through the focus of the parabola y2 = 4(x –1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then
A line L passing through the focus of the parabola y2 = 4(x –1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then
maths-General
maths-
The triangle formed by tangent to the parabola y = x2 at the point whose abscissa is x0 (where x0 
[1, 2]), the y-axis and the straight line y = x02 has the greatest area if x0 is equal to-
The triangle formed by tangent to the parabola y = x2 at the point whose abscissa is x0 (where x0 [1, 2]), the y-axis and the straight line y = x02 has the greatest area if x0 is equal to-
maths-General
maths-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
maths-General
maths-
If f (x) = 
and 
be the values of x, where f (f(x)) is not defined, then a ray of light parallel to the axis of the parabola y2 = 4x after reflection from the internal surface of the parabola will necessarily pass through the point.
If f (x) = and be the values of x, where f (f(x)) is not defined, then a ray of light parallel to the axis of the parabola y2 = 4x after reflection from the internal surface of the parabola will necessarily pass through the point.
maths-General
maths-
If the normal at three points (ap2, 2ap), (aq2, 2aq) and (ar2, 2ar) are concurrent then the common root of equations px2 + qx + r = 0 and a(b – c) x2 + b (c – a) x + c(a – b) = 0 is
If the normal at three points (ap2, 2ap), (aq2, 2aq) and (ar2, 2ar) are concurrent then the common root of equations px2 + qx + r = 0 and a(b – c) x2 + b (c – a) x + c(a – b) = 0 is
maths-General
physics-
A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
physics-General
physics-
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle 
to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle = 
will be
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle = will be
physics-General
physics-
A 2m long rod of negligible mass is free to rotate about its centre. An object of mass 5 kg is threaded into the rod at a distance of 50 cm from its end in such a way that the object can move without friction. The rod is then released from its horizontal position. The speed of the rod's end in the rod's vertical position is (in m/s)
A 2m long rod of negligible mass is free to rotate about its centre. An object of mass 5 kg is threaded into the rod at a distance of 50 cm from its end in such a way that the object can move without friction. The rod is then released from its horizontal position. The speed of the rod's end in the rod's vertical position is (in m/s)
physics-General
physics-
A uniform solid disc of mass 1 kg and radius 1m is kept on a rough horizontal surface. Two forces of magnitude 2 N and 4 N have been applied on the disc as shown in the figure. Linear acceleration of the centre of mass of the disc is if there is no slipping
A uniform solid disc of mass 1 kg and radius 1m is kept on a rough horizontal surface. Two forces of magnitude 2 N and 4 N have been applied on the disc as shown in the figure. Linear acceleration of the centre of mass of the disc is if there is no slipping
physics-General
physics-
A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of 
of its centre of mass and an angular velocity of 
. The distance (in m) of instantaneous axis of rotation from its centre of mass is
A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of of its centre of mass and an angular velocity of . The distance (in m) of instantaneous axis of rotation from its centre of mass is
physics-General
physics-
Three spools A, B and C are placed on rough ground and acted by equal force F. Then which of the following statement is incorrect?
Three spools A, B and C are placed on rough ground and acted by equal force F. Then which of the following statement is incorrect?
physics-General
physics-
A uniform thin stick of length 
and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is :
A uniform thin stick of length and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is :
physics-General
physics-
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Find the tension in the string when the block has maximum velocity.
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Find the tension in the string when the block has maximum velocity.
physics-General
physics-
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Maximum possible velocity of ring of mass ‘m’ is (Assuming zero friction):
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Maximum possible velocity of ring of mass ‘m’ is (Assuming zero friction):
physics-General
physics-
On producing the waves of frequency 1000 Hz in a Kundt’s tube, the total distance between 6 successive nodes is 
Speed of sound in the gas filled in the tube is
On producing the waves of frequency 1000 Hz in a Kundt’s tube, the total distance between 6 successive nodes is Speed of sound in the gas filled in the tube is
physics-General
