If e1and e2 are respectively the eccentricities of the ellipse 18x2+4y2=1 and the hyperbola 9x2−4y2=1, then the relation between e1and e2 is a.2e12+e22=3 b. e12+2e22=3 c. 2e12+e22=3 d. e12+3e22=2
For the hyperbola a2x2−b2y2=1 , let n be the number of points on the plane through which perpendicular tangents are drawn. If n=1,the==2 If n>1,then0<e<2 If n=0,the=>2 None of these
For hyperbola whose center is at (1, 2) and the asymptotes are parallel to lines 2x+3y=0 and x+2y=1 , the equation of the hyperbola passing through (2, 4) is (2x+3y−5)(x+2y−8)=40 (2x+3y−8)(x+2y−8)=40 (2x+3y−8)(x+2y−5)=30 none of these
A transvers axis cuts the same branch of a hyperbola a2x2−b2y2=1 at PandP′ and the asymptotes at Q and Q′ . Prove that PQ=P′Q′ and PQprime=PprimeQ˙
If PQ 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.
The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines
From a point P(1,2) , two tangents are drawn to a hyperbola H in which one tangent is drawn to each arm of the hyperbola. If the equations of the asymptotes of hyperbola H are 3x−y+5=0 and 3x+y−1=0 , then the eccentricity of H is (a)2(b) 32 (c) 2 (d) 3
Two tangents to the hyperbola a2x2−b2y2=1 having m1andm2 cut the axes at four concyclic points. Fid the value of m1m2˙