The ellipse x2+4y2=4is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is
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A tangent is drawn to the ellipse 27x2+y2=1 at (33cosθ,sinθ) where θϵ(0,2π)˙ Then find the value of θ such that the sum of intercepts on the axes made by this tangent is minimum.
Find the eccentricity of an ellipse a2x2+b2y2=1 whose latus rectum is half of its major axis. (a>b)
If the tangents to the ellipse a2x2+b2y2=1
make angles αandβ
with the major axis such that tanα+tanβ=γ,
then the locus of their point of intersection is
Find the equation for the ellipse that given that satisfies the given conditions: Length of minor axis 16, foci (0,±6).
Find the equation of the hyperbola satisfying the given conditions: Foci (± 5,0) the transverse axis 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.
Find the equation of tangents to the curve 4x2−9y2=1
which are parallel to 4y=5x+7.