A line passing through the origin O(0,0)
intersects two concentric circles of radii aandb
If the lines parallel to the X-and Y-axes through QandP,
respectively, meet at point R,
then find the locus of R˙
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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 .
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.
If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle
If the point (x,−1),(3,y),(−2,3),and(−3,−2)
taken in order are the vertices of a parallelogram, then find the values of xandy˙
Find the equation to which the equation
is transformed if the origin is shifted to the point (2,−3),
the axes remaining parallel to the original axies.
A rod AB of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. Show that the locus of P is an ellipse.
Find the equation of the circle with centre : (−a,b)and radius a2−b2.
If a vertex of a triangle is (1,1)
, and the middle points of two sides passing through it are −2,3)
then find the centroid and the incenter of the triangle.