If (x,y) is any point on the line joining (a,0) and (0,b), show that `x/a+y/b=1`

Any point on the line y = x is of the form

If each of the points (x_1,4),(-2,y_1) lies on the line joining the points (2,-1)a n d(5,-3) , then the point P(x_1,y_1) lies on the line.

If the points (x,y),(a,0) and (0,b) are collinear, prove that x/a + y/b = 1, ab ne 0

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

y = (ax-b)/((x-1)(x-4)) has a turning point P (2,-1). Find the values of 'a' and 'b' and show that y is maximum at P.

The length of projection of the line segment joining the points (1,0,-1) and (-1,2,2) on the plane x+3y-5z=6 is equal to

Find a point on the parabola y =(x-3)^2 , where the tangent is parallel to the line joining (3,0) and (4,1).

Find the length of the projection of the line segment joining the point A(-1,2,0) and B(1,-1,2) on the plane 2x-y-2z-4=0 .

In what ratio does the line y-x+2=0 cut the line joining (3, -1) and (8, 9) ?

Let (x,y) be any point on the parabola y^2= 4x . Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is: