Three normals to `y^2=4x` pass through the point (15, 12). Show that one of the normals is given by `y=x-3` and find the equation of the other.

Let L be a normal to the parabola y^2=4xdot If L passes through the point (9, 6), then L is given by

The normal lines to a given curve at each point (x,y) on the curve pass through the point (2,0) the curve passes through the point (2,3) formulate the differential equation representign the problem and hecne find the equation of the curve

Find the equation of a line passing through the point of intersection of the lines 4x+7y-3=0 and 2x-3y+1=0 that has equal intercepts on the axes.

Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

Three normals are drawn from the point (c, 0) to the curve y^2 = x . Show that c must be greater than 1/2. One normal is always the axis. Find c for which the other two normals are perpendicular to each other.

Find the equation of the curve passing through the origin if the middle point of the segment of its normal from any point of the curve to the x-axis lies on the parabola 2y^2=x

The equation of radical axis of two circles is x + y = 1 . One of the circles has the ends ofa diameter at the points (1, -3) and (4, 1) and the other passes through the point (1, 2).Find the equating of these circles.

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is