If the normals to the ellipse a2x2+b2y2=1 at the points (X1,y1),(x2,y2)and(x3,y3) are concurrent, prove that ∣∣x1x2x3y1y2y3x1y1x2y2x3y3∣∣=0.
Given the equation 4x2+23xy+2y2=1 . Through what angle should the axes be rotated so that the term xy is removed from the transformed equation.
Find the equation for the ellipse that satisfies the given conditions:Length of minor axis 16, foci (0,±6).
Let A=(3,4) and B is a variable point on the lines ∣x∣ =6. IF AB≤4 , then find the number of position of B with integral coordinates.
Find the locus of the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).
In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130o and ∠ECD = 20⊙ Find ∠BAC˙
Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4,3)and (−1,4).