Normals at two points `(x_(1),y_(1))and(x_(2),y_(2))` of the parabola `y^(2)=4x` meet again on the parabola, where `x_(1)+x_(2)=4`. Then `|y_(1)+y_(2)|` is equal to

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

The vertex of the parabola y^2 = 4x + 4y is

The vertex of the parabola y^2 + 4x = 0 is

The equation of the chord joining two points (x_(1),y_(1)) and (x_(2),y_(2)) on the rectangular hyperbola xy=c^(2) , is

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

The vertex of the parabola x^(2)=8y-1 is :

Statement 1: The normals at the points (4, 4) and (1/4,-1) of the parabola y^2=4x are perpendicular. Statement 2: The tangents to the parabola at the end of a focal chord are perpendicular.

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that (h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)) .

Find the point on the parabola y^(2) = 2x that is closest to the point (1, 4)

If three point A(x_(1), y_(1)), B(x_(2), y_(2)) and C(x_(3), y_(3)) will be collinear then the area of triangleABC= ____.