Find the slope of the normal at the point (am3 , am2 ) to the

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

Advertisement

61.

Find the slope of the normal at the point (am3 , am2 ) to the curve a x2 = y3.


The equation of the curve is a x2 = y3
Differentiating both sides w.r.t. x, we get,
                   2 ax space equals space 3 straight y squared dy over dx space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space space dy over dx space equals space fraction numerator 2 ax over denominator space 3 space straight y squared end fraction

At space left parenthesis am cubed comma space space space am squared right parenthesis comma space space dy over dx space equals space fraction numerator 2 straight a left parenthesis am cubed right parenthesis over denominator 3 left parenthesis am squared right parenthesis squared end fraction space space equals space fraction numerator 2 straight a squared straight m cubed over denominator 3 straight a squared straight m to the power of 4 end fraction space equals space fraction numerator 2 over denominator 3 space straight m end fraction
space therefore space space space space space space space At left parenthesis straight a space straight m cubed comma space space space straight a space straight m squared right parenthesis comma space space space slope space of space tangent space equals space fraction numerator 2 over denominator 3 straight m end fraction
therefore space space space space space space At left parenthesis am cubed comma space space am squared right parenthesis comma space space slope space of space normal space space equals space minus fraction numerator 1 over denominator begin display style fraction numerator 2 over denominator 3 straight m end fraction end style end fraction space equals space minus fraction numerator 3 straight m over denominator 2 end fraction

88 Views

Advertisement
62.

Find a point on the curve y = (x – 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

75 Views

63.

Find the point at which the tangent to the curve straight y equals space square root of 4 straight x minus 3 end root space minus 1 has its slope 2 over 3.

75 Views

64.

Find the equation of the normal to the curve y2 = 4x at the point (1, 2).

80 Views

Advertisement
65.

Find the equation of tangent to the ellipse straight x squared over straight a squared plus straight y squared over straight b squared space equals space 1 space space space at space left parenthesis straight x subscript 1 comma space space straight y subscript 1 right parenthesis.

88 Views

66.

Find the equation of tangent and normal to the hyperbola straight x squared over straight a squared minus straight y squared over straight b squared space equals space 1 space space at space space left parenthesis straight x subscript 0 comma space space straight y subscript 0 right parenthesis.

72 Views

67. Find the equation of the normal at the point (am2, am3) for the curve ay= x3.
94 Views

68.

Find the equation of the tangent and the normal to the curve straight x to the power of 2 over 3 end exponent plus straight y to the power of 2 over 3 end exponent space equals space 2 space space at space left parenthesis 1 comma space 1 right parenthesis

73 Views

Advertisement
69.

Find the equation of the tangent and normal to the curve  y2 = 4ax at the point (at2, 2at).

135 Views

 Multiple Choice QuestionsLong Answer Type

70. Find the equation of the tangent and normal to the curve
straight x space equals space 1 minus cos space straight theta comma space space space space space straight y space equals space straight theta minus sin space straight theta space space space space at space straight theta equals space straight pi over 4
83 Views

Advertisement