Determine the next term 20,24,33,49,74,110,?
Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x2+2xy+3y2+4x+8y−11=0 is tan−1(322)
If the pair of lines 3x2−4xy+3y2=0 is rotated about the origin by 6π in the anticlockwise sense, then find the equation of the pair in the new position.
If x2+2hxy+y2=0 represents the equation of the straight lines through the origin which make an angle α with the straight line y+x=0 (a)sec2α=h cosα (b)=(2h)(1+h) (c)2sinα =h(1+h) (d) cotα =(h−1)(1+h)
Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x3y+4=0.
If one of the lines denoted by the line pair ax2+2hxy+by2=0 bisects the angle between the coordinate axes, then prove that (a+b)2=4h2
Prove that the product of the perpendiculars from (α,β) to the pair of lines ax2+2hxy+by2=0 is (a−b)2+4h2aα2+2hαβ+bβ2