Find the value of k so that the area of teh triange with vertices A(k+1,1),B(4,−3) and C(7,−k) is 6 square units.
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˙
Find the locus of the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).
A straight line passing through P(3,1) meets the coordinate axes at AandB . It is given that the distance of this straight line from the origin O is maximum. The area of triangle OAB is equal to 350squ˙nits (b) 325squ˙nits 320squ˙nits (d) 3100squ˙nits
The line joining A(bcosαbsinα) and B(acosβ,asinβ) is produced to the point M(x,y) so that AM and BM are in the ratio b:a˙ Then prove that x+ytan(α+2β)=0.
OPQR is a square and M,N are the middle points of the sides PQandQR , respectively. Then the ratio of the area of the square to that of triangle OMN is 4:1 (b) 2:1 (c) 8:3 (d) 7:3
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.