If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P, then P is (a) (4,4) (b) (-1,

step 1 in this problem let us find the slope of the tangent to the graph by differentiating it you get

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Implicit Differentiation

This is a method used to find the derivative of a function defined by an equation where the dependent and independent variables are intermixed. It allows one to compute the slope of the tangent line to a curve when the curve is given in an implicit form, without first having to solve for one variable in terms of the other.

Tangent Line Construction

After determining the slope of the curve at a particular point using differentiation, the tangent line can be formed using the point-slope form of a line. This concept is fundamental in calculus and analytic geometry for approximating curves locally by their tangent lines.

Finding Intersection Points of Curves and Lines

When a line, such as a tangent, intersects its corresponding curve at another point, algebraic methods are used to solve for the coordinates of this intersection. This typically involves substituting the equation of the line into the equation of the curve and solving the resulting equation, often taking into account multiplicities that may arise from tangency.

Transcript

Please give Ace some feedback