are fixed straight lines, P
is any point and PM
are the perpendiculars from P
respectively. Find the locus of P
if the quadrilateral OMPN
is of constant area.
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The equation of conjugate axis of the hyperbola xy−3y−4x+7=0
(d) none of these
If the foci of the ellipse 16x2+b2y2=1
and the hyperbola 144x2−81y2=251
coincide, then find the value of b2
is the length of the latus rectum of the hyperbola for which x=3andy=2
are the equations of asymptotes and which passes through the point (4, 6), then the value of 2L
The equation ∣∣x2+(y−1)2−x2+(y+1)2∣∣=K
will represent a hyperbola for
The locus a point P(α,β) moving under the condition that the line y=αx+β is a tangent to the hyperbola a2x2−b2y2=1 is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle
Two circles are given such that they neither intersect nor touch. Then identify the locus of the center of variable circle which touches both the circles externally.
Show that the acute angle between the asymptotes of the hyperbola a2x2−b2y2=1,(a2>b2),
is the eccentricity of the hyperbola.
Find the coordinates of the foci, the eocentricity, the latus rectum, and the equations of directrices for the hyperbola 9x2−16y2−72x+96y−144=0