Three normals are drawn from the points (14,7) to the curve y2-16x-8y

1.	Three normals are drawn from the points (14,7) to the curve y2-16x-8y = 0 find the coordinatesof the feet of the normals.
Answer» Let the coordinates of foot of perprndicular be (x1,y1) Differentiating the equation to find the slope of the normal, => dy/dx = 8/(y-4) slope = -(dx/dy) hence we can find the equation of normal in terms of x1 and y1. then passing through the (x1,y1) thus we find a cubic equation on solving which we get, y1= 0, 16 , -4 thus corresponding x1 = 0, 8 , 3

Three normals are drawn from the points (14,7) to the curve y2-16x-8y = 0 find the coordinatesof the feet of the normals.

Answer»

Let the coordinates of foot of perprndicular be (x1,y1)

Differentiating the equation to find the slope of the normal,

=> dy/dx = 8/(y-4)

slope = -(dx/dy)

hence we can find the equation of normal in terms of x1 and y1.

then passing through the (x1,y1)

thus we find a cubic equation on solving which we get,

y1= 0, 16 , -4

thus corresponding x1 = 0, 8 , 3