Hyperbola questions
149 published questions with worked solutions.
- Let the eccentricity of the hyperbola H : x^ 2 /a^ 2 - y^ 2 /b^ 2 = 1 be 5/2 and length of its latus rectum be 6 2 . If y = 2x +...
- Let H : x^ 2 /a^ 2 - y^ 2 /b^ 2 = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the...
- The equation 2x^2-3y^2-6=0 represents
- Let H_n: x^2 1+n - y^2 3+n =1, n N. Let k be the smallest even value of n such that the eccentricity of H_k is a rational number....
- The foci of a hyperbola are ( 2, 0) and its eccentricity is 3 2 . A tangent, perpendicular to the line 2x + 3y = 6, is drawn at a...
- The vertices of a hyperbola H are ( 6, 0) and its eccentricity is 5 2 . Let N be the normal to H at point in the first quadrant...
- Let H be the hyperbola, whose foci are (1 2,0) and eccentricity is 2. Then the length of its latus rectum is ________.
- A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is
- Consider a branch of the hyperbola x^2 - 2y^2 - 2 2 x - 4 2 y - 6 = 0 with vertex at the point A. Let B be one of the end points...
- The locus of a point P( , ) moving under the condition that the line y = x + is a tangent to the hyperbola x^2 a^2 - y^2 b^2 = 1...
- For the hyperbola x^2 ^2 - y^2 ^2 = 1, which of the following remains constant when varies?
- If the line 4x+3y=7 touches the hyperbola x^2-y^2=7 then the sum of the co-ordinates of the point of contact is...
- If the line y=2x+ is a tangent to the hyperbola 36x^2-25y^2=3600, then =
- The locus of the points represented by |z+3|-|z-3|=6, where z is a complex number, is .
- The foci of a hyperbola coincide with the foci of the ellipse x^2 25 + y^2 9 =1. The equation of the hyperbola with eccentricity...
- The X and Y intercepts of the tangent to the hyperbola x^ 2 20 - y^ 2 5 =1 which is perpendicular to the line 4x+3y=7, are...
- If the tangent at the point (2 ,3 ) to the hyperbola x^2 4- y^2 9=1 is parallel to 3x-y+4=0, then the value of is
- The eccentricity of the hyperbola which passes through the points (3, 0) and (3 2 , 2) is
- If the eccentricity of a hyperbola x^2 9 - y^2 b^2 = 1, which passes through (K, 2), is 13 3 , then the value of K^2 is
- A tangent to the hyperbola x^2 4 - y^2 2 = 1 meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such that OPRQ is a...
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