Hyperbola questions
149 published questions with worked solutions.
- Let P(x_0, y_0) be the point on the hyperbola 3x^2-4y^2=36, which is nearest to the line 3x + 2y = 1. Then 2(y_0-x_0) is equal to...
- The line 2x + y = 1 is tangent to the hyperbola x^2 a^2 - y^2 b^2 = 1. If this line passes through the point of intersection of...
- Let the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4. If the hyperbola...
- Let P(6, 3) be a point on the hyperbola x^2 a^2 - y^2 b^2 = 1. If the normal at the point P intersects the x-axis at (9, 0), then...
- Tangents are drawn to the hyperbola x^2 9 - y^2 4 = 1, parallel to the straight line 2x − y = 1. The points of contact of the...
- Consider the hyperbola H:x^2-y^2=1 and a circle S with center N(x_2,0). Suppose that H and S touch each other at a point...
- If 2x-y+1=0 is a tangent to the hyperbola x^2 a^2 - y^2 16 =1, then which of the following CANNOT be sides of a right angled...
- The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is
- The equation of a tangent parallel to y = x drawn to x^2 3 - y^2 2 = 1, is
- The distance between the foci of the conic 7x^2 - 9y^2 = 63 is equal to
- The distance between the foci of the hyperbola x^2 - 3y^2 - 4x - 6y - 11 = 0 is
- If transverse and conjugate axes of hyperbola are equal then it's eccentricity is
- The one which does not represent a hyperbola is
- Distance between foci is 8 and distance between directrices is 6 of hyperbola, then length of latusrectum is
- A hyperbola, having the transverse axis of length 2 , is confocal with the ellipse 3x^2 + 4y^2 = 12. Then, its equation is
- The latusrectum of the hyperbola 9x^2 - 16y^2 + 72x - 32y - 16 = 0 is
- The distance between the directrices of the hyperbola x = 8 , y = 8 is
- For the hyperbola x^2 ^2 - y^2 ^2 = 1, which of the following remains constant when varies?
- If distance between directrices of a rectangular hyperbola is 10, then distance between its foci will be
- If t is a parameter, then x = a (t + 1 t ), y = b (t - 1 t ) represents
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