Rahul Bhujel

creator

6 Followers

Library Questions Stories About

Asked Questions

Find the condition that one of the lines ax2+2hxy+by2=0 may coincide with one of the lines a1x2+2h1xy+b1y2=0.

Find the condition that one of the lines ax2+2hxy+by2=0 may coincide with one of the lines a1x2+2h1xy+b1y2=0.

Prove that the two straight lines (x2+y2)sin2α=(xcosθ - ysinθ)2 include an angle 2α.

Find the equation to the pair of straight lines joining the origin to the intersection of the straight line y=mx+c and the curve x2+y2=a2. Prove that they are at right angles if 2c2=a2(1+m2).

If the line pairs ax2+2hxy+by2=0 and a'x2+2h'xy+b'y2=0 have the same bisectors, prove that h(a'-b')=h'(a-b).

Show that the lines joining the origin to the point of intersection of the line x + y = 1 with the curve 4x2+4y2+4x-2y-5=0 are at right angles to each other.

In a cyclic quadrilateral ABCD, CD is produced to E. If AD is the bisector of ∠𝐵𝐷𝐸, prove that △ 𝐴𝐵𝐶 is isosceles.