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.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Short Answer Type

61.

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

88 Views

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).

The equation of curve is
$straight y space equals space left parenthesis straight x minus 2 right parenthesis squared$
$therefore space space space space dy over dx space equals space 2 space left parenthesis straight x minus 2 right parenthesis therefore space space space space slope space of space tangent space equals space 2 left parenthesis straight x minus 2 right parenthesis$
Also slope of line joining (2, 0) and (4, 4) $equals space fraction numerator 4 minus 0 over denominator 4 minus 2 end fraction space equals space 4 over 2 space equals space 2$
$because space space tangent space is space parallel space to space the space line space joining space left parenthesis 2 comma space 0 right parenthesis space and space left parenthesis 4 comma space 4 right parenthesis therefore space space space their space slopes space are space equal therefore space space space space space 2 left parenthesis straight x minus 2 right parenthesis space equals space 2 space space space space space rightwards double arrow space space space space space straight x minus 2 space equals space 1 space space space space rightwards double arrow space space space straight x space equals space 3 When space straight x space equals space 3 comma space space space straight y space equals space left parenthesis 3 minus 2 right parenthesis squared space equals space 1 therefore space space space space space space required space point space is space left parenthesis 3 comma space 1 right parenthesis.$

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

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 ay²= x³.

94 Views

68.

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