A normal is drawn at a point `P(x , y)` of a curve. It meets the x-axis and the y-axis in point `A` AND `B ,` respectively, such that `1/(O A)+1/(O B)` =1, where `O` is the origin. Find the equation of such a curve passing through `(5, 4)`

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

A normal is drawn at a point P(x , y) of a curve. It meets the x-axis at Qdot If P Q has constant length k , then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^2-y^2) . Find the equation of such a curve passing through (0, k)dot

A normal is drwn at a point P(x,y) of a curve. It meets the x-axis at Q. If PQ is of constant length k, then show that the differential equation describing such curves is y(dy)/(dx)=+-sqrt(k^(2)-y^(2)) . Find the equation of such a curve passing through (0,k).

A curve y=f(x) passes through (1,1) and tangent at P(x , y) cuts the x-axis and y-axis at A and B , respectively, such that B P : A P=3, then (a) equation of curve is x y^(prime)-3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2, 1/8 (d) equation of curve is x y^(prime)+3y=0

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

The tangent at any point P to a curve C intersects the coordinate axes at A and B. If P be the mid-point of the line segment AB and the curve passes through the point (1,1), find the equation of the curve C.

A curve C has the property that if the tangent drawn at any point P on C meets the co-ordinate axis at A and B , then P is the mid-point of A Bdot The curve passes through the point (1,1). Determine the equation of the curve.

The slope of a curve at ( x,y) is 2x+1 . If the curve passes through the point (-4,2) , find the equation of the curve .

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

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