Find the equation of the tangent to the curve x2 + 3y = 3, whi

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 Multiple Choice QuestionsShort Answer Type

101. Find the point on the curve y = x3 – 11 x + 5 at which the tangent has the equation y = x – 11.
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102.

Find the point on the curve y = x3 – 2x2 – 2x at which the tangent lines are parallel to the line y = 2x – 3.

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103.

Find the points on the curve y = x3 – 2x2 – x at which the tangent lines are parallel to the line y = 3x – 2.

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104.

Find the equation of the tangent to the curve x2 + 3y = 3, which is parallel to the line y – 4x + 5 = 0. 


The equation of curve is x2 + 3y = 3                               ...(1)
Differentiating w.r.t.x, we get,
2 straight x plus 3 dy over dx space equals 0 space space space space rightwards double arrow space space space space dy over dx space equals space minus fraction numerator 2 straight x over denominator 3 end fraction
therefore space space space straight m subscript 1 space equals space minus fraction numerator 2 straight x over denominator 3 end fraction
Let space space straight m subscript 2 space be space slope space of space line space space straight y minus 4 straight x plus 5 space equals space 0
therefore space space space space space space straight m subscript 2 space equals 4
because space space space tangent space is space parallel space to space straight y minus 4 straight x plus 5 space equals space 0
therefore space space space space space space straight m subscript 1 space equals space straight m subscript 2
therefore space space space space space space space fraction numerator negative 2 straight x over denominator 3 end fraction space equals space 4 space space space space space space space space space space space space space space space space space rightwards double arrow space space space straight x space equals space minus 6
therefore space space space space space space from space left parenthesis 1 right parenthesis comma space space space 36 plus 3 straight y space equals space 3 space space space space rightwards double arrow space space space space straight y space equals space minus 11
therefore space space space point space is space left parenthesis negative 6 comma space minus 11 right parenthesis
therefore space space space space equation space of space tangent space at space left parenthesis negative 6 comma space minus 11 right parenthesis space is
space space space space space straight y plus 11 space equals space 4 left parenthesis straight x plus 6 right parenthesis space space space space or space space space space space space straight y plus 11 space equals space 4 straight x plus 24 space space space space space or space space space space 4 straight x minus straight y plus 13 space equals space 0

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105.

Find the equations of all lines having slope -1 that are tangents to the curve straight y equals fraction numerator 1 over denominator straight x minus 1 end fraction. straight x not equal to 1.

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106.

Find the equation of all lines having slope 2 and being tangent to the curve straight y plus fraction numerator 2 over denominator straight x minus 3 end fraction space equals space 0.

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 Multiple Choice QuestionsLong Answer Type

107.

Find the equation of all lines having 0 slope and that are tangent to the curve straight y equals fraction numerator 1 over denominator straight x squared minus 2 straight x plus 2 end fraction.

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 Multiple Choice QuestionsShort Answer Type

108.

Find the equation of the tangent to the curve straight y equals square root of 3 straight x minus 2 end root which is parallel to the line 4x - 2y + 5 = 0

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 Multiple Choice QuestionsLong Answer Type

109.

Find the equation of tangents to the curve
y = cos (x + y), – 2 straight pi ≤ x ≤ 2 straight pi
that are parallel to the line x + 2y = 0.

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110.

Find the point on curve 4x2 + 9y2 = 1, where the tangents are perpendicular to the line 2y + x = 0.

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