Hyperbola questions
149 published questions with worked solutions.
- A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis....
- Let 0 < < 2. If the eccentricity of the hyperbola x^2 ^2 - y^2 ^2 = 1 is greater than 2, then the length of its latus rectum lies...
- If the vertices of a hyperbola be at (−2, 0) and (2, 0) and one of its foci be at (−3, 0), then which one of the following points...
- If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the...
- The equation of a tangent to the hyperbola 4x^2 - 5y^2 = 20 parallel to the line x − y = 2 is:
- For 0 < θ < π/2, if the eccentricity of the hyperbola x^2 - y^2 ^2 = 5 is 7 times eccentricity of the ellipse x^2 ^2 + y^2 = 5,...
- Consider a hyperbola H having centre at the origin and foci on the x-axis. Let C_1 be the circle touching the hyperbola H and...
- If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then the equation of the normal to it at P is :
- A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x^2 4 - y^2 2 =1 at the point (x_1, y_1). Then...
- A hyperbola having the transverse axis of length 2 has the same foci as that of the ellipse 3x^2+4y^2=12, then this hyperbola...
- Let H : -x^2 a^2 + y^2 b^2 = 1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the...
- Let S be the focus of the hyperbola x^2 3 - y^2 5 = 1, on the positive x-axis. Let C be the circle with its centre at A(√6, √5)...
- Let P(3, 3) be a point on the hyperbola, x^2 a^2 - y^2 b^2 =1. if the normal to it at P intersects the x-axis at (9, 0) and e is...
- If the co-ordinates of two points A and B are ( 7 ,0) and (- 7 ,0) respectively and P is any point on the conic, 9x^2+16y^2=144,...
- If the line y = mx + c is a common tangent to the hyperbola x^2 100 - y^2 64 =1 and the circle x^2+y^2=36, then which one of the...
- The curve represented by Im (z^2 )=k, where k is a non-zero real number, is
- Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point of the line segment...
- Let H : x²/a² − y²/b² = 1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is...
- Let the eccentricity e of a hyperbola satisfy the equation 6e²−11e+3=0. If the foci of the hyperbola are (3,5) and (3,−4), then...
- The eccentricity of an ellipse E with centre at the origin O is √3/2 and its directrices are x=±4√6/3. Let H : x²/a²−y²/b²=1 be a...
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