Show that the curve for which the normal at every point passes through a fixed point is a circle. Find the equation of the circle if the normal at every point passes through the origin.
My Self Assessment
a) x2 + y2 = c
Solve (xy2 + 2x2y3) dx + (x2y – x3y2) dy = 0
Solve
Solve y (axy + ex) dx – ex dy = 0
Solve (x3ex – my2) dx + mxy dy = 0
Solve y (2x2y + ex) dx – (ex + y3) dy = 0
Solve x dx + y dy + (x2 + y2) dy = 0
Solve x dy – y dx = a (x2 + y2) dy
Solve (x2 + y2 + a2) y dy + x (x2 + y2 − a2) dx = 0
Solve ysin 2x dx – (1 + y2 + cos2x) dy = 0
Solve y (2xy + ex) dx = ex dy
Solve x dy – y dx + 3x4 dx = 0
Solve x dy – y dx = (x2 + y2) dx
Solve a (x dy +2y dx) = xy dy
Solve x dy – y dx + 2 (x2 + y2) dx = 0
Find the Cartesian equation of the curve whose gradient at (x, y) is and passes through the point (a, 2a)
Find the equation of the curve whose Cartesian subnormal is constant
Find the curve in which the Cartesian sub tangent varies inversely as the square of the abscissa.
Show that the curve in which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is a rectangular hyperbola.
The slope of the curve at any point is the reciprocal of twice the ordinate at the point. The curve also passes through the point (4, 3). Find its equation.
The normal PG to a curve meets the X–axis in G. If the distance of G from the origin is twice the abscissa of P, prove that the curve is a rectangular hyperbola.
Find the family of curves whose tangents form an angle with tangents to the hyperbola xy = c.
and passes through the point (a, 2a)
