If a point A(0,2) is equidistant from the points B(3,p) and C(p,5) then find the value of p.
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.
If (xi,yi),i=1,2,3, are the vertices of an equilateral triangle such that (x1+2)2+(y1−3)2=(x2+2)2+(y2−3)2=(x3+2)2+(y3−3)2, then find the value of y1+y2+y3x1+x2+x3 .
See Fig. 3.11 and complete the following statements:(i) The abscissa and the ordinate of the point B are _and _ Hence, the coordinates of B are (__,__).(ii) The x–coordinate and the y–coordinate of the point M are _ and _ respectively. Hence, the coordinates of M are (__,__).(iii) The x–coordinate and the y–coordinate of the point L are _ and _ respectively. Hence, the coordinates of L are (__,__).(iv) The .r–coordinate and the y–coordinate of the point S are _ and _ respectively. Hence, the coordinates of S are (__,__).
If (b2−b1)(b3−b1)+(a2−a1)(a3−a1)=0 , then prove that the circumcenter of the triangle having vertices (a1,b1),(a2,b2) and (a3,b3) is (2a2+a3,2b2+b3)
In ABC, if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of ABC) is (21,32) (b) (31,32) (32,1) (d) none of these
Given that P(3,1),Q(6.5), and R(x,y) are three points such that the angle PRQ is a right angle and the area of RQP is 7, find the number of such points R˙