α is root of the equation x2 – 5x + 6 = 0 and β is a root of the equation x2– x – 30 = 0, then coordinates of the point P farthest from the origin are
is farthest from the origin if P = (3, 6)
Find the equation of the curve 2x2 + y2 – 3x + 5y – 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.
Given the equation through what angle should the axes be rotated so that the term in xy be waiting from the transformed equation.
Find the locus of the point of intersection of the lines and where α is variable.
Find the locus of a point whose co – ordinate are given by x = t + t2, y = 2t + 1, where t is variable.
The points (a, b + c), (b, c + a) and (c, a + b) are
O(0, 0), P(–2, –2) and Q(1, –2) are the vertices of a triangle, R is a point on PQ such that PR : RQ
If three vertices of a rectangular are (0, 0), (a, 0) and (0, b), length of each diagonal is 5 and the perimeter 14, then the area of the rectangle is
If the line joining the points A(a2, 1) and B(b2, 1) is divides in the ratio b : a at the pint P whose x-coordinate is 7, their
If two vertices of a triangle are (3, –5) and (–7, 8) and centroid lies at the pint (–1, 1), third vertex of the triangle is at the point (a, b) then
are two points whose mid-point is at the origin. is a point on the plane whose distance from the origin is