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

81.

Show that the normal at any point 0 to the curve
x = a cosө + a ө sinө. y = a sin ө – a ө cos ө
is at a constant distance from the origin.

78 Views

82.

Find the equation of the tangent and normal to the given curves at the points given:
y = x² at (0,0).

76 Views

83.
Find the equation of the tangent and normal to the given curves at the points given:
y² = 4ax at (0, 0).

The equation of curve is y² = 4ax
Differentiating both sides w.r.t.x, $2 straight y dy over dx space equals space 4 straight a space space space space space space space rightwards double arrow space space space space space dy over dx space equals space fraction numerator 2 straight a over denominator straight y end fraction$
At (0, 0) $dy over dx$ does not exist
$therefore space space space space space tangent space at space left parenthesis 0 comma space 0 right parenthesis space is space vertical therefore space space space space its space equation space is space straight x space equals space 0$

89 Views

84.

Find the equation of the tangent and normal to the given curves at the points given:
y = x³ at (1, 1)

74 Views

85.

Find the equation of the tangent and normal to the given curves at the points given:
y = x² at (2, 8)

72 Views

Long Answer Type

86.

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

80 Views

Short Answer Type

87. Find the equation of the normal at the point (am², am³) for the curve ay²= x³.

83 Views

88.

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

84 Views

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

78 Views

Long Answer Type

90.

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