Find the equation of tangents to the curve 4x2−9y2=1 which are parallel to 4y=5x+7.
Determine the ratio in which the line 3x+y−9=0 divides the segment joining the points (1,3) and (2,7)˙
If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a2+1,a2+1) and (2a,−2a), then find the orthocentre.
Given the equation 4x2+23xy+2y2=1 . Through what angle should the axes be rotated so that the term xy is removed from the transformed equation.
Find the locus of the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).
AB is a variable line sliding between the coordinate axes in such a way that A lies on the x-axis and B lies on the y-axis. If P is a variable point on AB such that PA=b,Pb=a , and AB=a+b, find the equation of the locus of P˙