Chords of the ellipse a2x2+b2y2=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.
A variable line through the point P(2,1) meets the axes at AandB . Find the locus of the centroid of triangle OAB (where O is the origin).
Find the equation for the ellipse that satisfies the given conditions:Ends of major axis (±3,0), ends of minor axis (0,±2)
Find the coordinates of the point which divides the line segments joining the points (6,3) and (−4,5) in the ratio 3:2 (i) internally and (ii) externally.
If (1,4) is the centroid of a triangle and the coordinates of its any two vertices are (4,−8) and (−9,7), find the area of the triangle.
Write True or False: Give reasons for your answers.(i) Line segment joining the centre to any point on the circle is a radius of the circle.(ii) A circle has only finite number of equal chords.(iii) If a circle is divided into three equal arcs, each is a major arc.(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.(v) Sector is the region between the chord and its corresponding arc.(vi) A circle is a plane figure.
The equation of a curve referred to a given system of axes is 3x2+2xy+3y2=10. Find its equation if the axes are rotated through an angle 450 , the origin remaining unchanged.