The circle x2+y2−8x=0 and hyperbola 9x2−4y2=1 I intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
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The number of normal (s) of a rectangular hyperbola which can touch its conjugate is equal to
is a double ordinate of the hyperbola a2x2−b2y2=1
such that OPQ
is an equilateral triangle, O
being the center of the hyperbola, then find the range of the eccentricity e
of the hyperbola.
Referred to the principal axes as the axes of coordinates find the equation of the hyperbola whose foci are at (0,±10)
and which passes through the point (2,3)˙
The ellipse 25x2+16y2=1 and the hyperbola 25x2−16y2=1 have in common
Find the eccentricity of the hyperbola whose latusrectum is half of its transverse axis.
If P(a,b), the point of intersection of the ellipse a2x2+a2(1−e2)y2=1 and the hyperbola a2x2−a2(E2−1)y2=41 is equidistant from the foci of the two curves (all lying in the right of y-axis), then
Find the area of the triangle formed by any tangent to the hyperbola a2x2−b2y2=1
with its asymptotes.
Find the equation of the hyperbola whose foci are (6,4)and(−4,4) and eccentricity is 2.