Maths-
General
Easy
Question
The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is-
- x = – 1
- x = 1
- x = –
- x =
The correct answer is: x =
To find the equation of directrix.
+ 4y + 4x + 2 = 0
= – 4 [x – (1 / 2)]
Let y + 2 = Y and x – (1 / 2) = X
= – 4X
Here a = 1, the equation of the directrix is X = a.
x – (1 / 2) = 1
x = 3 / 2
Therefore, the equation of directrix is x = 3 / 2.
Related Questions to study
maths-
Let tangent at P (3, 4) to the parabola (y – 3)2 = (x – 2) meets line x = 2 at A and if S be the focus of parabola then 
is equal to
Let tangent at P (3, 4) to the parabola (y – 3)2 = (x – 2) meets line x = 2 at A and if S be the focus of parabola then is equal to
maths-General
Maths-
If two tangents drawn from the point (
) to the parabola y2 = 4x be such that the slope of one tangent is double of the other then
If two tangents drawn from the point () to the parabola y2 = 4x be such that the slope of one tangent is double of the other then
Maths-General
physics-
The temperature at which the speed of sound in air becomes double of its value at 
is
The temperature at which the speed of sound in air becomes double of its value at is
physics-General
physics-
A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10
. The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
A transverse sinusoidal wave moves along a string in positive x-direction at a speed of 10. The wavelength of the wave is 0.5 m and its amplitude is 10.cm at a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is
physics-General
maths-
The point on the line x – y + 2 = 0 from which the tangent to the parabola y2 = 8x is perpendicular to the given line is (a, b), then the line ax + by + c = 0 is
The point on the line x – y + 2 = 0 from which the tangent to the parabola y2 = 8x is perpendicular to the given line is (a, b), then the line ax + by + c = 0 is
maths-General
Maths-
The equation of normal in terms of slope m to the parabola (y – 2)2 = 4 (x – 3)
The equation of normal in terms of slope m to the parabola (y – 2)2 = 4 (x – 3)
Maths-General
maths-
The condition that the parabolas y2 = 4c (x – d) and y2 = 4ax have a common normal other then x-axis (a 
0, c 0) is
The condition that the parabolas y2 = 4c (x – d) and y2 = 4ax have a common normal other then x-axis (a 0, c 0) is
maths-General
physics-
If the speed of the wave shown in the figure is 
in the given medium, then the equation of the wave propagating in the positive 
-direction will be (all quantities are in M.K.S. units)
If the speed of the wave shown in the figure is in the given medium, then the equation of the wave propagating in the positive -direction will be (all quantities are in M.K.S. units)
physics-General
Maths-
The circle 
touches the parabola y2 = 4x externally. Then
The circle touches the parabola y2 = 4x externally. Then
Maths-General
physics-
The displacement-time graphs for two sound waves 
and 
are shown in the figure, then the ratio of their intensities 
is equal to
The displacement-time graphs for two sound waves and are shown in the figure, then the ratio of their intensities is equal to
physics-General
Maths-
The equations of the normals at the ends of the latus rectum of the parabola y2 = 4ax are given by
The equations of the normals at the ends of the latus rectum of the parabola y2 = 4ax are given by
Maths-General
physics-
The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency 
If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is
The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is
physics-General
physics-
An Indian submarine and an enemy submarine move towards each other during maneuvers in motionless water in the Indian ocean. The Indian submarine moves at 
and the enemy submarine at 
The Indian sub sends out a sonar signal (sound wave in water) at 
Sonar waves travel at 
What is the frequency detected by the Indian submarine
An Indian submarine and an enemy submarine move towards each other during maneuvers in motionless water in the Indian ocean. The Indian submarine moves at and the enemy submarine at The Indian sub sends out a sonar signal (sound wave in water) at Sonar waves travel at What is the frequency detected by the Indian submarine
physics-General
maths-
The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola is-
The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola is-
maths-General
Maths-
Let F be the focus of the parabola y2 = 4ax and M be the foot of perpendicular from point P(at2, 2at) on the tangent at the vertex. If N is a point on the tangent at P then 
equals -
Let F be the focus of the parabola y2 = 4ax and M be the foot of perpendicular from point P(at2, 2at) on the tangent at the vertex. If N is a point on the tangent at P then equals -
Maths-General
