Prove that chord of contact of ellipse a2x2+b2y2=1 w.r.t. any point on the directrix is focal chord.
If the foci of an ellipse are (0,±1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.
From any point P lying in the first quadrant on the ellipse 25x2+16y2=1,PN is drawn perpendicular to the major axis and produced at Q so that NQ equals to PS, where S is a focus. Then the locus of Q is 5y−3x−25=0 3x+5y+25=0 3x−5y−25=0 (d) none of these
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 4x2+9y2=36
Prove that the area bounded by the circle x2+y2=a2 and the ellipse a2x2+b2y2=1 is equal to the area of another ellipse having semi-axis a−b and b,a>b .
Find the equation of the hyperbola satisfying the given conditions: Foci (±35,0) the latus rectum is of length 8
Find the equation of the parabola that satisfies the following conditions: Focus (0,−3); directrix y=3
The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 21, then find the locus of the focus.