Hyperbola
Showing 50 of 106 · 106 total
- 1.The eccentricity of an ellipse E with centre at the origin O is √32 and its directrices ar…Medium
- 2.Let e_1 and e_2 be two distinct roots of the equation x^2-ax+2=0.Hard
- 3.If the eccentricity e of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, passing through (6,4 √3)…Medium
- 4.Let the eccentricity e of a hyperbola satisfy the equation 6e^2-11e+3=0.Medium
- 5.Let H:x^2a^2-y^2b^2=1 be a hyperbola such that the distance between its foci is 6 and the …Medium
- 6.Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such t…Medium
- 7.Let the ellipse E: (x^2)/(144) + (y^2)/(169) = 1 and the hyperbola H: (x^2)/(16) - (y^2)/(…Medium
- 8.Let PQ be a chord of the hyperbola (x^2)/(4)-(y^2)/(b^2)=1, perpendicular to the x -axis s…Medium
- 9.Let the domain of the function f(x)= _3 _5 _7(9x-x^2-13) be the interval (m,n).Medium
- 10.Let P(10,2√15) be a point on the hyperbola x^2a^2-y^2b^2=1, whose foci are S and S^'.Medium
- 11.If the line x+2y=1, where R, does not meet the hyperbola x^2-9y^2=9, then a possible value…Medium
- 12.Let the foci of a hyperbola coincide with the foci of the ellipse (x^2)/(36)+(y^2)/(16)=1.Medium
- 13.Let e1 and e2 be the eccentricities of the ellipse (x^2)/(b^2) + (y^2)/(25) = 1 and the hy…Medium
- 14.Let the sum of the focal distances of the point P(4,3) on the hyperbola H:x^2a^2-y^2b^2=1 …Hard
- 15.Let one focus of the hyperbola H:x^2a^2-y^2b^2=1 be at (√10,0) and the corresponding direc…Medium
- 16.Let the foci of a hyperbola be (1,14) and (1,-12).Medium
- 17.Let the foci of a hyperbola H coincide with the foci of the ellipse [E: ((x-1)^2)/(100)+((…Medium
- 18.Let H:-x^2a^2+y^2b^2=1 be the hyperbola, whose eccentricity is √3 and the length of the la…Medium
- 19.Consider a hyperbola H having centre at the origin and foci on the x-axis.Medium
- 20.For 0< < /2, if the eccentricity of the hyperbola x^2-y^2 ^2 =5 is √7 times eccentricity o…Medium
- 21.If the foci of a hyperbola are same as that of the ellipse [(x^2)/(9)+(y^2)/(25)=1] and th…Hard
- 22.Let P be a point on the hyperbola [H: (x^2)/(9)-(y^2)/(4)=1], in the first quadrant such t…Medium
- 23.Let e_1 be the eccentricity of the hyperbola [(x^2)/(16)-(y^2)/(9)=1] and e_2 be the eccen…Medium
- 24.Let R be a rectangle given by the lines x=0,x=2,y=0 and y=5.Medium
- 25.Let H be the hyperbola, whose foci are (1 √2,0) and eccentricity is √2.Easy
- 26.The locus of the point of intersection of the straight lines, tx - 2y - 3t = 0 x - 2ty + 3…Medium
- 27.For some (0,( )/(2)), let the eccentricity and the length of the latus rectum of the hyper…Medium
- 28.Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2 …Medium
- 29.Consider the hyperbola x^2a^2-y^2b^2=1 having one of its focus at P(-3,0).Hard
- 30.If the equation of the hyperbola with foci (4,2) and (8,2) is 3x^2-y^2- x+ y+ =0, then + +…Medium
- 31.Let the product of the focal distances of the point P(4,2√3) on the hyperbola H:x^2a^2-y^2…Medium
- 32.Let H_1:x^2a^2-y^2b^2=1 and H_2:-x^2A^2+y^2B^2=1 be two hyperbolas having length of latus …Medium
- 33.Let S be the focus of the hyperbola x^23-y^25=1, on the positive x-axis.Medium
- 34.The length of the latus rectum and directrices of hyperbola with eccentricity e are 9 and …Hard
- 35.Let the foci and length of the latus rectum of an ellipse [(x^2)/(a^2)+(y^2)/(b^2)=1, a>b …Medium
- 36.Let the latus rectum of the hyperbola [(x^2)/(9)-(y^2)/(b^2)=1] subtend an angle of [()/(3…Hard
- 37.The foci of a hyperbola are [( 2,0)] and its eccentricity is [(3)/(2)].Medium
- 38.Let m_1 and m_2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola…Medium
- 39.Let H_n:x^21+n-y^23+n=1,n N.Medium
- 40.Let the eccentricity of an ellipse [x^2a^2+y^2b^2=1] is reciprocal to that of the hyperbol…Medium
- 41.If the line x+2y=1, where R, does not meet the hyperbola x^2-9y^2=9, then a possible value…Medium
- 42.Let PQ be a chord of the hyperbola x^24-y^2b^2=1, perpendicular to the x-axis, such that O…Medium
- 43.Let O be the origin, and P and Q be two points on the rectangular hyperbola xy=12 such tha…Medium
- 44.If the eccentricity of the hyperbola x^2a^2-y^2b^2=1, passing through (6,4√3), satisfies 1…Medium
- 45.Let e_1 and e_2 be two distinct roots of x^2-ax+2=0.Hard
- 46.Let H_1:x^2a^2-y^2b^2=1 and H_2:y^2B^2-x^2A^2=1 be two hyperbolas having lengths of latus …Medium
- 47.If the equation of the hyperbola with foci (4,2) and (8,2) is 3x^2-y^2- x+ y+=0, then ++ i…Medium
- 48.Let P(x_0,y_0) be the point on the hyperbola 3x^2-4y^2=36 which is nearest to the line 3x+…Medium
- 49.Let the eccentricity of the hyperbola x^2a^2-y^2b^2=1 be 54.Medium
- 50.The normal to the hyperbola x^2a^2-y^29=1 at the point (8,3√3) on it passes through the po…Medium