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)`

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 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 drawn at a point P(x,y) of a curve. It meets the x-axis at Q such that PQ is of constant length k . Find coordinates of q also find equation of curve

Tangent is drawn at any point P of a curve which passes through (1, 1) cutting x-axis and y-axis at A and B respectively. If AP: BP = 3:1 , then,

A line is drawn from a point P(x, y) on the curve y = f(x), making an angle with the x-axis which is supplementary to the one made by the tangent to the curve at P(x, y). The line meets the x-axis at A. Another line perpendicular to it drawn from P(x, y) meeting the y-axis at B. If OA = OB, where O is the origin, theequation of all curves which pass through ( 1, 1) is

If the line 5x + 12y - 60 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is:

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

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

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

If the point 3x+4y-24=0 intersects the X -axis at the point A and the Y -axis at the point B , then the incentre of the triangle OAB , where O is the origin, is