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Application Of Derivatives

Question
CBSEENMA12035239
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The line y = x + 1 is a tangent to the curve y 2 = 4x at the point

  • (1, 2)

  • (2, 3)

  • (1, -2)

  • (-1, 2)

Solution

A.

(1, 2)

The equation of curve is straight y squared space equals space 4 straight x
therefore space space space space space space 2 straight y dy over dx space equals space 4 space space space space space space or space space space space dy over dx space equals space 2 over straight y comma space space space space space which space is space slope space of space tangent space to space the space curve.
Consider the tangent line y =x+1
Its slope = 1
From given condition,
           2 over straight y space equals space 1 space space space space space or space space space straight y space equals space 2
When y = 2,   4 = 4x    rightwards double arrow    x = 1
therefore space space space space space point space is space left parenthesis 1 comma space 2 right parenthesis therefore space space space space space left parenthesis straight A right parenthesis space is space correct space answer.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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