`A(x_1,y_1),B(x_2,y_2)` are the given points. Find the locus of P such that `angleAPB = 90^@`.

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

The optimal solution of an L.P.P. occurs at two distinct points (x_1,y_1) and (x_2,y_2) of the feasible region. Will this solution occur at some other point also.

Statement 1 :If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2 : The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

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.

Find the equations of the tangent and normal to the curve 16x^2 + 9y^2 = 145 at (x_1, y_1) , where x_1=2 and y_1>0 . Also find the points of intersection where both tangent and normal cut the x-axis.

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.

Find the distance between P (x_1, y_1) and Q (x_2, y_2) when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.

The ordinates of points P and Q on the parabola y^2 = 12x are in the ratio 1 : 2. Find the locus of the point of intersection of the normals to the parabola at P and Q.