Find the points on the ellipse 4x2+9y2=1 on which the normals are parallel to the line 2x−y=1.
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.
Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.
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 foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.25x2+100y2=1
Find the equation of the circle passing through the points (2,3)and (−1,1)and whose centre is on the line x−3y−11=0.
Angle of a line with the positive direction of the x-axis is θ . The line is rotated about some point on it in anticlockwise direction by angle 450 and its slope becomes 3. Find the angle θ˙