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

71. Find the equation of the tangent and normal to the curve x = a t² , y = 2 at at the point ‘t’.

90 Views

Long Answer Type

72. Find the equation of the tangent at

straight t space equals space straight pi over 4 space to space the space curve space straight x space equals sin space 3 straight t comma space space space space space straight y space equals space cos 2 straight t.

73 Views

Short Answer Type

73.

Find the equation of tangent to the curve given by x = a sin³ t, y = b cos³ t at a point where $straight t equals space straight pi over 2.$

102 Views

Long Answer Type

74.

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

73 Views

75.

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

74 Views

76.

Find the equation of tangent to the curve:
$straight x space equals space 1 plus cos space straight theta comma space space space space straight y equals space straight theta plus sinθ space space at space straight theta space equals space straight pi over 4.$

72 Views

77.
Find the equation of the tangent and normal to the curve
$straight x space equals space cost comma space space space space space straight y space equals space sin space straight t space space space at space straight t space equals space straight pi over 4$

The equations of the curve are $straight x space equals space cos space straight t comma space space space space straight y space equals space sin space straight t$    $At space space space straight t space equals space straight pi over 4 comma space space space straight x space equals space cos space straight pi over 4 space equals space fraction numerator 1 over denominator square root of 2 end fraction comma space space space straight y space equals space sin space straight pi over 4 space equals space fraction numerator 1 over denominator square root of 2 end fraction$
$therefore space space space space point space of space contact space is space open parentheses fraction numerator 1 over denominator square root of 2 end fraction comma space space space space fraction numerator 1 over denominator square root of 2 end fraction close parentheses$
Also,    $dx over dt space equals space minus sin space straight t comma space space space dy over dt space equals space cot space space space space space space space space space space space rightwards double arrow space space space space dy over dx space equals space fraction numerator begin display style dy over dx end style over denominator begin display style dx over dt end style end fraction space equals space fraction numerator cos space straight t over denominator negative sin space straight t end fraction space equals space minus cot space straight t$
$At space straight t space equals space straight pi over 4 comma space space space dy over dx space equals space minus cot straight pi over 4 space equals space minus 1$

$therefore space space space space space space at space straight t space equals space straight pi over 4 comma space space slope space of space tangent space space equals space minus 1$
$therefore space space space space the space equation space of space tangent space at space straight t space equals space straight pi over 4 space is space$
$straight y minus fraction numerator 1 over denominator square root of 2 end fraction space equals space minus 1 open parentheses straight x minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses space space space space space or space space space space space straight y minus fraction numerator 1 over denominator square root of 2 end fraction space equals space minus straight x plus fraction numerator 1 over denominator square root of 2 end fraction$
or    $straight x plus straight y minus square root of 2 space equals space 0$
Also slope of normal = $negative fraction numerator 1 over denominator negative 1 end fraction space equals space 1$
$therefore space space space space space equation space of space normal space at space straight t space equals space straight pi over 4 space is$
$straight y minus fraction numerator 1 over denominator square root of 2 end fraction space equals space 1 open parentheses straight x minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses space space space space or space space space space straight x minus straight y space equals space 0$

78 Views

Short Answer Type

78.

Find the equation of the tangent to the curve
$straight y space equals space fraction numerator 1 plus sinx over denominator cosx end fraction space at space straight x space equals space straight pi over 4.$