The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point
Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16
If the normal at one end of the latus rectum of the ellipse a2x2+b2y2=1 passes through one end of the minor axis, then prove that eccentricity is constant.
Tangents are drawn from the points on a tangent of the hyperbola x2−y2=a2 to the parabola y2=4ax˙ If all the chords of contact pass through a fixed point Q, prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.
Find the point (α,β) on the ellipse 4x2+3y2=12, in the first quadrant, so that the area enclosed by the lines y=x,y=β,x=α , and the x-axis is maximum.
The tangent at a point P on an ellipse intersects the major axis at T,andN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on NT as diameter intersects the auxiliary circle orthogonally.
Find the equation of the locus of the middle points of the chords of the hyperbola 2x2−3y2=1, each of which makes an angle of 450 with the x-axis.