If a leaf of a book is folded so that one corner moves along an opposite side, then prove that the line of crease will always touch parabola.

The lower corner of a leaf in a book is folded over so as to reach the inner edge of the page. Show that the fraction of the width folded over when the area of the folded part is minimum is 2/3.

One side of a rectangular piece of paper is 6cm, the adjacent sides being longer than 6cms. One corner of the paper is folded so that it sets on the opposite longer side.If the length of the crease is lcms and it makes an angle theta with the long side as shown,then l is

If a circle br drawn so as always to touch a given straight line and also a given circle externally then prove that the locus of its centre is a parabola.

Prove that the straight line x+y=1 touches the parabola y=x-x^(2)

If one angle of a triangle is equal to one angle of another triangle and bisector of these equal angles divide the opposite side in the same ratio; prove that the triangles are similar.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.

Prove that line joining the midpoints of opposite sides of a quadrilateral bisect each other.

The normals at P,R,R on the parabola y^(2)=4ax meet in a point on the line y=c . Prove that the sides of the triangle PQR touch the parabola x^(2)=2cy

A cubical room has dimensions 4 ft xx 4 ft xx 4 ft . An insect starts from one corner O and reaches a corner on the opposite side of the body diagonal. In previous problem, the magnitude of displacement is :

Prove that for thetainR , the line y=(x-11)costheta-cos3theta is always normal to the parabola y^(2)=16x .