Maths-
General
Easy
Question
The abcissa and ordinate of the end points A and B of a focal chord of the parabola y2 = 4x are respectively the roots of x2 – 3x + a = 0 and y2 + 6y + b = 0. The equation of the circle with AB as diameter is.
- x2 + y2 – 3x + 6y + 3 = 0
- x2 + y2 – 3x + 6y – 3 = 0
- x2 + y2 + 3x + 6y – 3 = 0
- x2 + y2 – 3x – 6y – 3 = 0
The correct answer is: x2 + y2 – 3x + 6y – 3 = 0
t1 t2 = – 1 as AB is focal chord
x2 – 3x + a = 0 ; x1 + x2 = 3 & x1x2 = a
y2 + 6y + b = 0 ; y1 + y2 = – 6 & y1y2 = b
x1x2 = 
. t12 = 1 = a
y1y2 = 2t1
= – 4 = b
a = 1, b = – 4
equation of circle AB is diameter
x2 + y2 – 3x + 6y – 3 = 0
Related Questions to study
physics-
A particle of mass m is moving along the side of a square of side 'a', with a uniform speed 
in the x-y plane as shown in the figure: Which of the following statements is false for the angular momentum L 
about the origin?
A particle of mass m is moving along the side of a square of side 'a', with a uniform speed in the x-y plane as shown in the figure: Which of the following statements is false for the angular momentum L about the origin?
physics-General
physics-
A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force 
is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C
A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C
physics-General
physics-
The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is
The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is
physics-General
physics-
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure Momentum of both the blocks are equal at time t = ....seconds :
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure Momentum of both the blocks are equal at time t = ....seconds :
physics-General
physics-
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure. If coefficient of friction between the two blocks is equal to 0.4, then magnitude of initial slope of 
versus t and 
versus t (in SI unit) will be :–
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure. If coefficient of friction between the two blocks is equal to 0.4, then magnitude of initial slope of versus t and versus t (in SI unit) will be :–
physics-General
physics-
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure. The correct graph showing linear momentum of 1 kg (i.e. ) and of 2kg (i.e. ) versus time is
A 1 kg block is given a velocity of 15 m/s towards right over a very long rough plank of mass 2 kg as shown in figure. The correct graph showing linear momentum of 1 kg (i.e. ) and of 2kg (i.e. ) versus time is
physics-General
physics-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is 
at time t, then the displacement of the second block at this instant is :-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is at time t, then the displacement of the second block at this instant is :-
physics-General
physics-
Two blocks of equal mass m are connected by an Un stretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is at time t, then the displacement of the first block at this instant is :
Two blocks of equal mass m are connected by an Un stretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is at time t, then the displacement of the first block at this instant is :
physics-General
physics-
Two blocks of equal mass m are connected by an unstretched spring, and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure Then the displacement of the centre of mass at time t is:-
Two blocks of equal mass m are connected by an unstretched spring, and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure Then the displacement of the centre of mass at time t is:-
physics-General
physics-
An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass 
and piece B with mass 
. Two pieces then move across the floor along x–axis. Graph of position versus time for the two pieces are given If all the graphs are possible then, in which of the following cases external force must be acting on the box :-
An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass and piece B with mass . Two pieces then move across the floor along x–axis. Graph of position versus time for the two pieces are given If all the graphs are possible then, in which of the following cases external force must be acting on the box :-
physics-General
physics-
An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass and piece B with mass . Two pieces then move across the floor along x–axis. Graph of position versus time for the two pieces are given. Which graphs pertain to physically possible explosions ?
An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass and piece B with mass . Two pieces then move across the floor along x–axis. Graph of position versus time for the two pieces are given. Which graphs pertain to physically possible explosions ?
physics-General
physics-
When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by 
Here 
is the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/s. Total mass of gas is 20 kg. Coefficient of friction between the car and road is 
= 0.1 Car will stop after (from starting) t = .... seconds :
When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by Here is the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/s. Total mass of gas is 20 kg. Coefficient of friction between the car and road is = 0.1 Car will stop after (from starting) t = .... seconds :
physics-General
physics-
When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by Here is the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/total mass of gas is 20 kg. Coefficient of friction between the car and road is = 0.1 Maximum speed of car will be v = ..... m/s 
When the mass of a system is variable, a thrust force has to be applied on it in addition to all other forces acting on it. This thrust force is given by Here is the relative velocity with which the mass dm either enters or leaves the system. A car has total mass 50 kg. Gases are ejected from this backwards with relative velocity 20 m/s. The rate of ejection of gas is 2 kg/total mass of gas is 20 kg. Coefficient of friction between the car and road is = 0.1 Maximum speed of car will be v = ..... m/s
physics-General
physics-
The minimum audible wavelength at room temperature is about
The minimum audible wavelength at room temperature is about
physics-General
physics-
Two open organ pipes gives 4 beats/sec when sounded together in their fundamental nodes. If the length of the pipe are 
and 
respectively, then the velocity of sound is :
Two open organ pipes gives 4 beats/sec when sounded together in their fundamental nodes. If the length of the pipe are and respectively, then the velocity of sound is :
physics-General
