Find the locus of the point of intersection of tangents to the ellipse if the difference of the eccentric angle of the points is 32π˙
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Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.9y2−27x2=1
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.y2=12x x2=−16yy2=10x
A rod AB of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and end point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. Show that the locus of P is an ellipse.
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas:(i) 9x2−16y2=1 (ii) y2−16x2=1
into its equivalent Cartesian equation.
The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5)
. Find the equation referred to the original axes.
Find the equation for the ellipse that satisfies the given conditions:Length of major axis 26, foci (±5,0)
is a variable point on the lines ∣x∣
=6. IF AB≤4
, then find the number of position of B
with integral coordinates.