Hyperbola
Showing 50 of 106 · 106 total
- 51.Let the eccentricity of the hyperbola H:x^2a^2-y^2b^2=1 satisfy 1+b^2a^2=52, and let the l…Medium
- 52.Let a>0, b>0.Medium
- 53.Let H:x^2a^2-y^2b^2=1, a>0,b>0, be a hyperbola such that the sum of the lengths of the tra…Medium
- 54.Let the foci of the ellipse x^216+y^27=1 and the hyperbola x^2144-y^2=125 coincide.Medium
- 55.If the line x-1=0 is a directrix of the hyperbola kx^2-y^2=6, then the hyperbola passes th…Medium
- 56.Let the hyperbola H:x^2a^2-y^2b^2=1 pass through the point (2√2,-2√2).Medium
- 57.A hyperbola passes through the foci of the ellipse x^225+y^216=1 and its transverse and co…Medium
- 58.The locus of the centroid of the triangle formed by any point P on the hyperbola 16x^2-9y^…Medium
- 59.The point P(-2√6,√3) lies on the hyperbola x^2a^2-y^2b^2=1 having eccentricity √52.Medium
- 60.If a hyperbola passes through the point P(10,16) and it has vertices at (6,0), then the eq…Medium
- 61.If e_1 and e_2 are the eccentricities of the ellipse x^218+y^24=1 and the hyperbola x^29-y…Medium
- 62.If the line y=mx+c is a common tangent to the hyperbola x^2100-y^264=1 and the circle x^2+…Medium
- 63.A line parallel to the straight line 2x-y=0 is tangent to the hyperbola x^24-y^22=1 at the…Medium
- 64.For some (0,2), if the eccentricity of the hyperbola x^2-y^2^2=10 is √5 times the eccentri…Medium
- 65.A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis,…Medium
- 66.Equation of a common tangent to the parabola y^2=4x and the hyperbola xy=2 is:Medium
- 67.If the vertices of a hyperbola be at (-2,0) and (2,0) and one of its foci be at (-3,0), th…Medium
- 68.If a hyperbola has length of its conjugate axis equal to 5 and the distance between its fo…Medium
- 69.Let 0<<2.Medium
- 70.A hyperbola has its centre at the origin, passes through the point (4,2) and has transvers…Medium
- 71.If a directrix of a hyperbola centred at the origin and passing through the point (4,-2√3)…Medium
- 72.If the line y=mx+7√3 is normal to the hyperbola x^224-y^218=1, then a value of m is:Medium
- 73.If the eccentricity of the standard hyperbola passing through the point (4,6) is 2, then t…Medium
- 74.A hyperbola passes through the point P(√2,√3) and has foci at (2,0).Medium
- 75.The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the l…Medium
- 76.If the eccentricity of a hyperbola x^29-y^2b^2=1, which passes through (k,2), is √133, the…Easy
- 77.For the hyperbola x^2^2-y^2^2=1, which of the following remains constant when varies?Medium
- 78.The locus of a point P(,) moving under the condition that the line y= x+ is a tangent to t…Medium
- 79.The normal to a curve at P(x,y) meets the x-axis at G.Medium
- 80.A hyperbola whose transverse axis is along the major axis of the conic, [x^2 3 + y^2 4 = 4…Medium
- 81.Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whos…Medium
- 82.Tangents are drawn to the hyperbola 4x2 - y2 = 36 at the points P and Q.Medium
- 83.A normal to the hyperbola, 4x2 - 9y2 = 36 meets the co-ordinate axes x and y at A and B, r…Hard
- 84.If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the …Medium
- 85.The locus of the point of intersection of the lines, [ 2 x - y + 4 2 k = 0] and [ 2 k,x + …Medium
- 86.If 5x + 9 = 0 is the directrix of the hyperbola 16x2 -- 9y2 = 144, then its corresponding …Medium
- 87.The equation of a tangent to the hyperbola 4x2 -- 5y2 = 20 parallel to the line x -- y = 2…Easy
- 88.Let e1 and e2 be the eccentricities of the ellipse, [x^2 25 + y^2 b^2 = 1(b < 5) and the h…Medium
- 89.A hyperbola having the transverse axis of length [ 2 ] has the same foci as that of the el…Medium
- 90.Let P(3, 3) be a point on the hyperbola, [x^2 a^2 - y^2 b^2 = 1].Medium
- 91.If e1 and e2 are the eccentricities of the ellipse, [x^2 18 + y^2 4 = 1] and the hyperbola…Medium
- 92.The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to th…Medium
- 93.Consider a hyperbola H : x2 - 2y2 = 4.Medium
- 94.Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x2 - y2 = 3.Medium
- 95.The locus of the centroid of the triangle formed by any point P on the hyperbola 16x^2 - 9…Medium
- 96.The locus of the mid points of the chords of the hyperbola x2 - y2 = 4, which touch the pa…Medium
- 97.Let the tangent drawn to the parabola y^2=24 x at the point [(, )] is perpendicular to the…Medium
- 98.Let the eccentricity of the hyperbola [H:x^2 a^2 - y^2 b^2 = 1] be [ 5 2 ] and length of i…Medium
- 99.Let [P(x_0, y_0)] be the point on the hyperbola 3 x^2-4 y^2=36, which is nearest to the li…Medium
- 100.Let T and C respectively be the transverse and conjugate axes of the hyperbola 16x^2 - y^2…Medium