Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is
The locus of the mid points of the chords passing through a fixed point (a, b) of the hyperbola, is
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The locus of the foot of the perpendicular from the centre of the hyperbola xy = c^{2} on a variable tangent is
The equation to the chord joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) on the rectangular hyperbola xy = c^{2} is
The equation 9x^{2}  16y^{2}  18x + 32y  15 = 0 represent a hyperbola
From the points of the circle x^{2} + y^{2} = a^{2}, tangents are drawn to the hyperbola x^{2} – y^{2} = a^{2}; then the locus of the middle points of the chords of contact is
The tangent to the hyperbola xy = c^{2} at the point P intersects the xaxis at T and the yaxis at T'. The normal to the hyperbola at P intersects the xaxis at N and the yaxis at N'. The areas of the triangles PNT and PNT' are D and D' respectively, then is
The asymptote of the hyperbola form with any tangent to the hyperbola a triangle whose area is a^{2} tan l in magnitude then its eccentricity is
From any point on the hyperbola H_{1} : (x^{2}/a^{2})  (y^{2}/b^{2}) = 1 tangents are drawn to the hyperbola .H_{2} : (x^{2}/a^{2})  (y^{2}/b^{2}) = 2. The area cutoff by the chord of contact on the asymptotes of H_{2} is equal to
The tangent at P on the hyperbola (x^{2} / a^{2})  (y^{2} / b^{2}) = 1 meets the asymptote at Q. If the locus of the mid point of PQ has the equation (x^{2} / a^{2})  (y^{2} / b^{2}) = k, then k has the value equal to
The tangent to the hyperbola, x^{2}  3y^{2} = 3 at the point (√3, 0) when associated with two asymptotes constitutes.
If θ is the angle between the asymptotes of the hyperbola with eccentricity e, then sec θ/2 can be
If (5, 12) and (24, 7) are the focii of a conic passing through the origin then the eccentricity of conic is
The point of contact of 5x + 12y = 19 and x^{2} – 9y^{2} = 9 will lie on
Equation (2 + λ)x^{2}  2λxy + (λ  1)y^{2}  4x  2 = 0 represents a hyperbola if
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447 docs930 tests
