Show that the area of the triangle inscribed in the parabola `y^2= 4ax` is : `(1)/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))|` , where `y_(1),y_(2),y_(3)` are the ordinates of the angular points.

Show that the equation of the tangent to the parabola y^(2) = 4 ax at (x_(1), y_(1)) is y y_(1) = 2a(x + x_(1)) .

If y_1, y_2, y_3 be the ordinates of a vertices of the triangle inscribed in a parabola y^2=4a x , then show that the area of the triangle is 1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot

Find the co-ordinates of the centroid of the triangle whose vertices are (x_(1),y_(1),z_(1)), (x_(2),y_(1),z_(2)) and (x_(3),y_(3),z_(3)) .

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

The three points (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)), (x_(3), y_(3), z_(3)) are collinear when…………

The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)le1-x} is

A circle cuts the rectangular hyperbola xy=1 in the points (x_(r),y_(r)), r=1,2,3,4 . Prove that x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1

Find the area of the regionn bounded by y = -1, y = 2, x= y^3 and x= 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.

if y= sin mx, them the value of the determinant |{:(y,,y_(1),,y_(2)),(y_(3),,y_(4),,y_(5)),(y_(6),,y_(7),,y_(8)):}|" Where " y_(n)=(d^(n)y)/(dx^(n)) " is "