Find the equation of the normal to the curve x^2=4 y, which passes through the point (1,2)

Name: Problem 13, Chapter 8: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2021-06-06T13:06:57-08:00
Duration: 1 min 38 s
Channel: Dharmendra Jain
Description: Find the equation of the normal to the curve x^2=4 y, which passes through the point (1,2)

step 1 In this question we have to find the equation of the normal to the curve y equals y square is eq

Find the equation of the normal to the curve x^2=4 y, which...

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Key Concepts

Implicit Differentiation

Implicit differentiation is a technique used to differentiate equations where the dependent and independent variables are intermingled, rather than expressed explicitly as a function. It is essential for finding the derivative of curves defined by equations such as the one given, thereby allowing the calculation of the tangent and normal slopes.

Differentiation

Differentiation is the process of finding the rate at which a function changes at any given point. It is used to compute the slope of the tangent line to a curve by calculating the derivative, which measures the instantaneous rate of change of the function.

Tangent Line

The tangent line to a curve at a specific point is the straight line that just touches the curve at that point, having the same slope as the curve. It is primarily determined using the derivative of the function at the given point.

Normal Line

The normal line to a curve at a given point is the line perpendicular to the tangent line at that point. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the normal can be obtained by taking the negative reciprocal of the tangent’s slope.

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