Find alll curves in the xy plane for which the normal at each point (x,y) intersects the x axis at (1+x,0).
Answers
Answered by
4
The normal to the curve y = f(x) at P (x1, y1) intersects the x axis at (1+x1 , 0).
Let the normal be : y = m x + c
then, y1 = m x1 + c
and 0 = m (1+x1) + c => c = - m - m x1
Then y1 = -m,
m = slope of normal at P(x, y) = - y
So, Slope of tangent at P(x,y) = 1/y = d y / d x
So, d y/ d x = 1/ y or, y dy = dx then
integrating both sides, y² /2 = x + K1 or y² = 2 x + K
=============================================
Let the normal be : y = m x + c
then, y1 = m x1 + c
and 0 = m (1+x1) + c => c = - m - m x1
Then y1 = -m,
m = slope of normal at P(x, y) = - y
So, Slope of tangent at P(x,y) = 1/y = d y / d x
So, d y/ d x = 1/ y or, y dy = dx then
integrating both sides, y² /2 = x + K1 or y² = 2 x + K
=============================================
kvnmurty:
did u understand? u r in which class?
Similar questions