Hyperbola questions
149 published questions with worked solutions.
- Let the foci of hyperbola coincide with the foci of the ellipse x^2 36 + y^2 16 = 1. If the eccentricity of the hyperbola is 5,...
- If the line x + 2y = 1, where R , does not meet the hyperbola x^2 - 9y^2 = 9, then a possible value of is:
- Let P(10,2 15 ) be a point on the hyperbola x^2 a^2 - y^2 b^2 =1, whose foci are S and S'. If the length of its latus rectum is...
- Let the domain of the function f(x) = _3 _5 _7(9x - x^2 - 13) be the interval (m, n). Let the hyperbola x^2 a^2 - y^2 b^2 = 1...
- For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x^2 - y^2 ^2 = 8 be e_1 and _1,...
- Let the ellipse E: x^2 144 + y^2 169 =1 and the hyperbola H: x^2 16 - y^2 ^2 =-1 have the same foci. If e and L respectively...
- Let E: x^2 a^2 + y^2 b^2 =1, a > b and H: x^2 A^2 - y^2 B^2 =1. Let the distance between the foci of E and the foci of H be 2 3....
- Let H_1 : x^2 a^2 - y^2 b^2 =1 and H_2 : x^2 A^2 + y^2 B^2 =1 be two hyperbolas having length of latus rectums 15 2 and 12 5...
- Let one focus of the hyperbola H : x^2 a^2 - y^2 b^2 = 1 be at ( 10 , 0) and the corresponding directrix be x = 9 10 . If e and l...
- If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x^2 - y^2 - x + y + = 0, then + + is equal to _____.
- Let the product of the focal distances of the point (4, 2 3) on the hyperbola H : x^2 a^2 - y^2 b^2 =1 be 32. Let the length of...
- The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to...
- A hyperbola passes through the point P( 2 , 3 ) and has foci at (±2, 0). Then the tangent to this hyperbola at P also passes...
- Tangents are drawn to the hyperbola 4x^2 - y^2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then...
- If the eccentricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the tangent to the...
- If the line y = mx + 7 3 is normal to the hyperbola x^2 24 - y^2 18 = 1, then a value of m is:
- If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 - 9y^2 = 144, then its corresponding focus is:
- If the tangent drawn to the hyperbola 4y^2 = x^2 + 1 intersect the co-ordinate axes at the distinct points A and B, then the...
- A normal to the hyperbola, 4x^2 - 9y^2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram...
- If a directrix of a hyperbola centred at the origin and passing through the point (4, -2 3) is 5x = 4 5 and its eccentricity is...
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