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Equations of Tangents and Normals using Differentiation Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

FAQs on Equations of Tangents and Normals using Differentiation Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the equation of the tangent line using differentiation?
The equation of the tangent line to a curve at a given point can be found using differentiation. It is given by the equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the point of tangency and m is the slope of the tangent line.
2. How do you find the equation of the normal line using differentiation?
To find the equation of the normal line to a curve at a given point, differentiate the equation of the curve and find the slope of the tangent line using differentiation. Then, find the negative reciprocal of the tangent line's slope to get the slope of the normal line. Finally, use the point of tangency to write the equation of the normal line in the form y - y₁ = m(x - x₁).
3. What is the relationship between the tangent and normal lines?
The tangent line is a line that touches the curve at a specific point, while the normal line is a line that is perpendicular to the tangent line at that same point. The tangent line and normal line at a given point have slopes that are negative reciprocals of each other.
4. How do you determine the slope of the tangent line using differentiation?
To determine the slope of the tangent line at a given point, differentiate the equation of the curve with respect to the independent variable. Then, substitute the x-coordinate of the point into the derivative to find the slope.
5. Can you find the equation of the tangent line without using differentiation?
Yes, the equation of the tangent line can also be found without using differentiation. If the equation of the curve is known, the slope of the tangent line can be determined at a given point by finding the derivative of the curve equation and substituting the x-coordinate of the point. Then, the equation of the tangent line can be written using the point-slope form.
204 videos|288 docs|139 tests

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