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The equation of normal in terms of slope m to the parabola (y – 2)² = 4 (x – 3)

y = mx – 2m – m³
y = mx – 5m – m³ + 2
y – 2 = mx – 2m – m³
none of these

The correct answer is: y = mx – 5m – m³ + 2

To find the equation of normal.
Given , parabola (Y – 2)2 = 4 (X – 3)
Using equation of normal to parabola $y squared equals space 4 a x space$ is $y space equals space m x space minus 2 a m space minus m cubed$ .
Here comparing the equations of parabola we get a = 1; y = (Y – 2) and x = (X – 3)
Then substitute them in $y space equals space m x space minus 2 a m space minus m cubed$
$Y minus 2 space equals space m left parenthesis X minus 3 right parenthesis space minus 2 left parenthesis 1 right parenthesis m space minus m cubed Y minus 2 space equals space m X space minus 3 m minus 2 m minus m cubed Y equals space m X space minus 5 m minus m cubed space plus 2$

Therefore, Using equation of normal to parabola $y squared equals space 4 a x space$ is $y space equals space m x space minus 2 a m space minus m cubed$ y = mx – 5m – m3 + 2 is the equation of normal in terms of slope.

The condition that the parabolas y² = 4c (x – d) and y² = 4ax have a common normal other then x-axis (a $greater than$ 0, c $greater than$ 0) is

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If the speed of the wave shown in the figure is $330 m divided by s$ in the given medium, then the equation of the wave propagating in the positive $x$ -direction will be (all quantities are in M.K.S. units)

physics-General

General

Maths-

The circle $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 lambda x equals 0 comma lambda element of R$ touches the parabola y² = 4x externally. Then

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General

physics-

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $I subscript A end subscript divided by I subscript B end subscript$ is equal to

physics-General

General

Maths-

The equations of the normals at the ends of the latus rectum of the parabola y² = 4ax are given by

Maths-General

General

physics-

The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency $600 blank H z.$ If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is

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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 $50 blank k m divided by h comma$ and the enemy submarine at $70 blank k m divided by h.$ The Indian sub sends out a sonar signal (sound wave in water) at $1000 blank H z.$ Sonar waves travel at $5500 blank k m divided by h.$ What is the frequency detected by the Indian submarine

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maths-

The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola is-

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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 $fraction numerator M N over denominator F N end fraction$ equals -

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General

Maths-

If the point (2a, a) lies inside the parabola x² – 2x – 4y + 3 = 0, then a lies in the interval -

Maths-General

General

Maths-

If the chord of contact of tangents from a point P to the parabola y² = 4ax touches the parabola x² = 4by, the locus of P is -

Maths-General

General

Maths-

Let A be the vertex and L the length of the latus rectum of the parabola y² – 2y – 4x – 7 = 0. The equation of the parabola with A as vertex, 2L the length of the latus rectum and the axis at right angles to that of the given curve is -

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biology

Given below is the ECG of a normal human. Which one of its components is correctly interpreted below ?

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biology

Cords of bill roth are found in–

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Find the area of shaded region in the figure.

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The equation of normal in terms of slope m to the parabola (y – 2)2 = 4 (x – 3)

y = mx – 2m – m3 y = mx – 5m – m3 + 2 y – 2 = mx – 2m – m3 none of these

The correct answer is: y = mx – 5m – m3 + 2

To find the equation of normal.Given , parabola (Y – 2)2 = 4 (X – 3)Using equation of normal to parabola is .Here comparing the equations of parabola we get a = 1; y = (Y – 2) and x = (X – 3)Then substitute them in

Related Questions to study

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

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)

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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

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Let A be the vertex and L the length of the latus rectum of the parabola y2 – 2y – 4x – 7 = 0. The equation of the parabola with A as vertex, 2L the length of the latus rectum and the axis at right angles to that of the given curve is -

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The equation of normal in terms of slope m to the parabola (y – 2)² = 4 (x – 3)

y = mx – 2m – m³
y = mx – 5m – m³ + 2
y – 2 = mx – 2m – m³
none of these

The correct answer is: y = mx – 5m – m³ + 2

The condition that the parabolas y² = 4c (x – d) and y² = 4ax have a common normal other then x-axis (a $greater than$ 0, c $greater than$ 0) is

The condition that the parabolas y² = 4c (x – d) and y² = 4ax have a common normal other then x-axis (a $greater than$ 0, c $greater than$ 0) is

If the speed of the wave shown in the figure is $330 m divided by s$ in the given medium, then the equation of the wave propagating in the positive $x$ -direction will be (all quantities are in M.K.S. units)

If the speed of the wave shown in the figure is $330 m divided by s$ in the given medium, then the equation of the wave propagating in the positive $x$ -direction will be (all quantities are in M.K.S. units)

The circle $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 lambda x equals 0 comma lambda element of R$ touches the parabola y² = 4x externally. Then

The circle $x to the power of 2 end exponent plus y to the power of 2 end exponent plus 2 lambda x equals 0 comma lambda element of R$ touches the parabola y² = 4x externally. Then

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $I subscript A end subscript divided by I subscript B end subscript$ is equal to

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $I subscript A end subscript divided by I subscript B end subscript$ is equal to

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

The driver of a car travelling with speed 30 metres per second towards a hill sounds a horn of frequency $600 blank H z.$ 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 $600 blank H z.$ If the velocity of sound in air is 330 metres per second, the frequency of the reflected sound as heard by the driver is

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 $fraction numerator M N over denominator F N end fraction$ 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 $fraction numerator M N over denominator F N end fraction$ equals -

If the point (2a, a) lies inside the parabola x² – 2x – 4y + 3 = 0, then a lies in the interval -

If the point (2a, a) lies inside the parabola x² – 2x – 4y + 3 = 0, then a lies in the interval -

If the chord of contact of tangents from a point P to the parabola y² = 4ax touches the parabola x² = 4by, the locus of P is -

If the chord of contact of tangents from a point P to the parabola y² = 4ax touches the parabola x² = 4by, the locus of P is -

Let A be the vertex and L the length of the latus rectum of the parabola y² – 2y – 4x – 7 = 0. The equation of the parabola with A as vertex, 2L the length of the latus rectum and the axis at right angles to that of the given curve is -

Let A be the vertex and L the length of the latus rectum of the parabola y² – 2y – 4x – 7 = 0. The equation of the parabola with A as vertex, 2L the length of the latus rectum and the axis at right angles to that of the given curve is -