Maths-
General
Easy

Question

The tangent at (t, t squared – t cubed) on the curve y = x squared – x cubed meets the curve again at Q, then abscissa of Q must be -

  1. 1 + 2t    
  2. 1 – 2t    
  3. –1 –2t    
  4. 2t – 1    

Hint:

Slope of tangent = fraction numerator d y over denominator d x end fraction
find equation of tangent at P, then find the intersection point of the tangent and curve by substituting the given values in the option, and whosoever satisfies the equation is the required point.

The correct answer is: 1 – 2t


    Given : y = x squared – x cubed  and Point P(tt squared – t cubed)
    S l o p e space equals fraction numerator d y over denominator d x end fraction space equals space 2 x space minus space 3 x squared
A t space p o i n t space left parenthesis t comma space t squared space – space t cubed right parenthesis
rightwards double arrow fraction numerator d y over denominator d x end fraction space equals space 2 t space minus space 3 t squared
    Equation of tangent at point P
    rightwards double arrow y space minus left parenthesis space t squared space minus t cubed right parenthesis space equals space left parenthesis 2 t space minus space 3 t squared right parenthesis left parenthesis x minus t right parenthesis
rightwards double arrow y space minus space t squared space plus space t cubed space equals space x t left parenthesis 2 minus 3 t right parenthesis space minus 2 t squared space plus space 3 t cubed
rightwards double arrow y space equals space x t left parenthesis 2 minus 3 t right parenthesis space minus space t squared space space plus space 2 t cubed
    Find intersection point of the tangent and the curve by equating values of y for curve and tangent
    rightwards double arrow x squared space minus x cubed space equals space x left parenthesis 2 t space minus 3 t squared right parenthesis space plus space 2 t cubed space minus t squared
rightwards double arrow space space x cubed minus space x squared space plus space x left parenthesis 2 t space minus space 3 t squared right parenthesis space plus space t squared left parenthesis 2 t space minus space 1 right parenthesis space equals space 0
f o r space x space equals space 2 t plus 1
rightwards double arrow 8 t cubed space plus space 1 space plus space 12 t squared space plus space 6 t space minus space 4 t squared space minus 1 space minus 4 t space plus 4 t squared space minus 6 t cubed space plus 2 t space minus space 3 t squared space plus 2 t cubed space minus t squared space equals space d o e s n o t space s a t i s f y

    for x = 1-2t
    rightwards double arrow 1 minus space 8 t cubed space minus 6 t space plus 12 t squared space minus 1 minus 4 t squared space plus 4 t space plus 2 t minus 3 t squared space minus 4 t squared space plus 6 t cubed space plus 2 t cubed space minus t squared space equals space 0
T h u s space i t space s a t i s f i e s space left parenthesis 1 minus 2 t right parenthesis

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    Maths-

    If fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction = 1 is a tangent to the curve x = 4t,y =fraction numerator 4 over denominator t end fraction, t element of R then -

    If fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction = 1 is a tangent to the curve x = 4t,y =fraction numerator 4 over denominator t end fraction, t element of R then -

    Maths-General
    General
    Maths-

    The line fraction numerator x over denominator a end fraction + fraction numerator y over denominator b end fraction = 1 touches the curve y = be-x/a at the point :

    The line fraction numerator x over denominator a end fraction + fraction numerator y over denominator b end fraction = 1 touches the curve y = be-x/a at the point :

    Maths-General
    General
    physics

    An object moves in a straight line. It starts from the rest and its acceleration is . 2 ms2.After reaching a certain point it comes back to the original point. In this movement its acceleration  is -3 ms2, till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.

    An object moves in a straight line. It starts from the rest and its acceleration is . 2 ms2.After reaching a certain point it comes back to the original point. In this movement its acceleration  is -3 ms2, till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.

    physicsGeneral
    General
    Maths-

    For the ellipse fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma the foci are

    For the ellipse fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma the foci are

    Maths-General
    General
    Maths-

    For the ellipse fraction numerator x to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1, the latus rectum is

    For the ellipse fraction numerator x to the power of 2 end exponent over denominator 1 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1, the latus rectum is

    Maths-General
    General
    Maths-

    The sum of distances of any point on the ellipse 3 x2 + 4y2 = 24 from its foci is

    The sum of distances of any point on the ellipse 3 x2 + 4y2 = 24 from its foci is

    Maths-General
    General
    Maths-

    The equations x = a open parentheses fraction numerator 1 minus t to the power of 2 end exponent over denominator 1 plus t to the power of 2 end exponent end fraction close parentheses semicolon y equals fraction numerator 2 b t over denominator 1 plus t to the power of 2 end exponent end fraction semicolon t element of R represent

    The equations x = a open parentheses fraction numerator 1 minus t to the power of 2 end exponent over denominator 1 plus t to the power of 2 end exponent end fraction close parentheses semicolon y equals fraction numerator 2 b t over denominator 1 plus t to the power of 2 end exponent end fraction semicolon t element of R represent

    Maths-General
    General
    Maths-

    The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent

    The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent

    Maths-General
    General
    Maths-

    The line y = 2x + c touches the ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1 if c is equal to

    The line y = 2x + c touches the ellipse fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1 if c is equal to

    Maths-General
    General
    Maths-

    The eccentricity of the conic 3x2 + 4y2 = 24 is

    The eccentricity of the conic 3x2 + 4y2 = 24 is

    Maths-General
    General
    Maths-

    The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity fraction numerator 1 over denominator 2 end fraction is

    The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity fraction numerator 1 over denominator 2 end fraction is

    Maths-General
    General
    Maths-

    The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if

    The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if

    Maths-General
    General
    Maths-

    On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

    On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

    Maths-General
    General
    Maths-

    An ellipse has OB as a semi – minor axis, F, F¢ are its foci and the angle FBF¢ is a right angle. Then the eccentricity of the ellipse is

    An ellipse has OB as a semi – minor axis, F, F¢ are its foci and the angle FBF¢ is a right angle. Then the eccentricity of the ellipse is

    Maths-General
    General
    Maths-

    The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 – 30y = 0 is

    The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 – 30y = 0 is

    Maths-General