The locus of the midde points ofchords of hyperbola 3x2−2y2+4x−6y=0 parallel to y=2x is
Given that A(1,1) and B(2,−3) are two points and D is a point on AB produced such that AD=3AB˙ Find the coordinates of D˙
If A(cosα,sinα),B(sinα,−cosα),C(1,2) are the vertices of ABC, then as α varies, find the locus of its centroid.
Shift the origin to a suitable point so that the equation y2+4y+8x−2=0 will not contain a term in y and the constant term.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
The line joining the points (x,2x)and(3,5) makes an obtuse angle with the positive direction of the x-axis. Then find the values of x˙
Orthocenter and circumcenter of a DeltaABC are (a,b)and(c,d) , respectively. If the coordinates of the vertex A are (x1,y1), then find the coordinates of the middle point of BC˙