Maths-
General
Easy

Question

At any point P space open parentheses x subscript 1 comma y subscript 1 close parentheses on a curve if the subtangent and subnormal are equal then at that point the length of the tangent is equal to

  1. y subscript 1 end subscript    
  2. square root of 2 y subscript 1 end subscript    
  3. square root of 2 y subscript 1 end subscript end root    
  4. 2 y subscript 1 end subscript    

Hint:

We are given that the length of the subtangent and subnormal of a curve are equal at point P. We have to find the length of tangent.

The correct answer is: square root of 2 y subscript 1 end subscript


    The given point where the  subtangent and subnormal is equal is  (x1, y1).
    Subtangent is the projection of tangent on x-axis.
    Subnormal is the projection of normal on x-axis.
    The formula of subtangent is fraction numerator y over denominator fraction numerator d y over denominator d x end fraction end fraction
    The formula of subnormal is y fraction numerator d y over denominator d x end fraction
    The formula for length of tangent at point (x1, y1)
    L e n g t h space o f space tan g e n t space equals space open vertical bar y subscript 1 square root of 1 plus open parentheses fraction numerator d x over denominator d y end fraction close parentheses subscript x subscript 1 comma y subscript 1 end subscript end root close vertical bar
    Subtangent = Subnormal
    fraction numerator y over denominator fraction numerator d y over denominator d x end fraction end fraction equals y fraction numerator d y over denominator d x end fraction
space y over y equals open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared
1 space equals space open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared
1 space equals space open parentheses fraction numerator d x over denominator d y end fraction close parentheses squared
open parentheses fraction numerator d x over denominator d y end fraction close parentheses squared space equals space 1
    L e n g t h space o f space tan g e n t space equals open vertical bar y subscript 1 square root of 1 plus open parentheses fraction numerator d x over denominator d y end fraction close parentheses squared end root close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals vertical line y subscript 1 square root of 1 space plus space 1 end root vertical line
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals y subscript 1 square root of 2
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 2 y subscript 1

    This is the required answer.

    For such questions, we should know the formula of length of tangent, subnormal and subtangent.

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    biology

    The below diagram represents the human digestive system. Identify A, B, C, D and E

    The below diagram represents the human digestive system. Identify A, B, C, D and E

    biologyGeneral
    General
    physics

    A vessels of depth t is half filled with oil of refractive index n subscript 1 and the other half is filled with water (refractive index n subscript 2 ). The apparent depth of the vessel when viewed from above is…….

    A vessels of depth t is half filled with oil of refractive index n subscript 1 and the other half is filled with water (refractive index n subscript 2 ). The apparent depth of the vessel when viewed from above is…….

    physicsGeneral
    General
    physics

    A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n.P.  is a small object at a height h above the mirror. An observer 0, vertically above  P, outside the liquid sees P and its image in the mirror. The apparent distance between these two wall be.

    A plane mirror is placed at the bottom of a tank containing a liquid of refractive index n.P.  is a small object at a height h above the mirror. An observer 0, vertically above  P, outside the liquid sees P and its image in the mirror. The apparent distance between these two wall be.

    physicsGeneral
    General
    Maths-

    The length of the normal to the curve y equals a c o s space h open parentheses x over a close parentheses at any point varies as

    The length of the normal to the curve y equals a c o s space h open parentheses x over a close parentheses at any point varies as

    Maths-General
    General
    physics

    A ray of light is incident on one  equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true?

    A ray of light is incident on one  equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true?

    physicsGeneral
    General
    physics

    A ray of light is incident normally on one of the faces of a proms of apex 30 to the power of 0  and  n=square root of 2 what is the angle of deeviation which of the following is true?

    A ray of light is incident normally on one of the faces of a proms of apex 30 to the power of 0  and  n=square root of 2 what is the angle of deeviation which of the following is true?

    physicsGeneral
    General
    physics

    There is a prism with refractive index equal to square root of 2 and the refracting angle equal to 30 to the power of 0. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is.........

    There is a prism with refractive index equal to square root of 2 and the refracting angle equal to 30 to the power of 0. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is.........

    physicsGeneral
    General
    physics

    The minimum angle of deviation of a prism of refractive index 1.732  is equal to its refracting angle. What is the angle of prism?

    The minimum angle of deviation of a prism of refractive index 1.732  is equal to its refracting angle. What is the angle of prism?

    physicsGeneral
    General
    physics

    An equilateral prism deviates a ray through 45 to the power of 0 for two angles of incidence differing by 20 to the power of 0 . What is the nof the prism?

    An equilateral prism deviates a ray through 45 to the power of 0 for two angles of incidence differing by 20 to the power of 0 . What is the nof the prism?

    physicsGeneral
    General
    physics

    The minimum deviation produced by a glass prism of angle 60 to the power of 0  is  30 to the power of 0. If the velocity of light in vaccum is 3 cross times 10 to the power of 8 space end exponent m divided by s. Then what is the velocity of light in glass in m/s ?

    The minimum deviation produced by a glass prism of angle 60 to the power of 0  is  30 to the power of 0. If the velocity of light in vaccum is 3 cross times 10 to the power of 8 space end exponent m divided by s. Then what is the velocity of light in glass in m/s ?

    physicsGeneral
    General
    physics-

    Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of V volt. If one of the capacitor is completely immersed in a liquid of dielectric constant K, then the potential difference between the plates of the other capacitor will change to

    In series combination, charge is constant.
    therefore blank V proportional to fraction numerator 1 over denominator C end fraction
    Now, fraction numerator V subscript 2 end subscript over denominator V subscript 1 end subscript end fraction equals fraction numerator K C over denominator C end fraction equals fraction numerator K over denominator 1 end fraction
    But V subscript 1 end subscript plus V subscript 2 end subscript blank equals V
    or fraction numerator V subscript 2 end subscript over denominator K end fraction plus V subscript 2 end subscript blank equals V blank o r blank V subscript 2 end subscript equals fraction numerator K over denominator K plus 1 end fraction V

    Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of V volt. If one of the capacitor is completely immersed in a liquid of dielectric constant K, then the potential difference between the plates of the other capacitor will change to

    physics-General
    In series combination, charge is constant.
    therefore blank V proportional to fraction numerator 1 over denominator C end fraction
    Now, fraction numerator V subscript 2 end subscript over denominator V subscript 1 end subscript end fraction equals fraction numerator K C over denominator C end fraction equals fraction numerator K over denominator 1 end fraction
    But V subscript 1 end subscript plus V subscript 2 end subscript blank equals V
    or fraction numerator V subscript 2 end subscript over denominator K end fraction plus V subscript 2 end subscript blank equals V blank o r blank V subscript 2 end subscript equals fraction numerator K over denominator K plus 1 end fraction V
    General
    physics

    Angle of prism is A and its one surface is silvered. Light rays falling at an angle at incidence 2 A on first surface return back through the same path after suffering reflection at second silvered surface What is the refractive index of material?

    Angle of prism is A and its one surface is silvered. Light rays falling at an angle at incidence 2 A on first surface return back through the same path after suffering reflection at second silvered surface What is the refractive index of material?

    physicsGeneral
    General
    physics

    A light ray is incident perpendicular to one face of  90 to the power of 0 prism and is totally internally reflected at the glass-air interface. If the angle of reflection is  45 to the power of 0. We conclude that the refractive index....
    .

    A light ray is incident perpendicular to one face of  90 to the power of 0 prism and is totally internally reflected at the glass-air interface. If the angle of reflection is  45 to the power of 0. We conclude that the refractive index....
    .

    physicsGeneral
    General
    biology

    The below diagram is a duct system of liver, gall bladder and pancreas. Write the names of ducts from A to D

    The below diagram is a duct system of liver, gall bladder and pancreas. Write the names of ducts from A to D

    biologyGeneral
    General
    physics

    A ray falls on a prism  ABC(AB=BC) and travels as shown in the figure. The minimum refractive, index of the prism material should be.

    A ray falls on a prism  ABC(AB=BC) and travels as shown in the figure. The minimum refractive, index of the prism material should be.

    physicsGeneral