Hyperbola JEE Advanced Quiz
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Question 1 of 15
1. Question
3 pointsThe midpoint of the chord 4x−3y=5 of the hyperbola 2x^{2}−3y^{2}=12 is ?
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Question 2 of 15
2. Question
3 pointsIf the line lx+my=1 is a normal to the hyperbola, b^{2}x^{2}−a^{2}y^{2}=a^{2}b^{2}, then (a^{2}/l^{2})−(b^{2}/m^{2}) is equal to
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Question 3 of 15
3. Question
3 pointsThe tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola 5x^{2}−4y^{2}=20, meets xaxis and yaxis at A and B respectively. Then (OA)^{2}−(OB)^{2}, where O is the origin, equals:
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Question 4 of 15
4. Question
3 pointsThe area (in square units) of the equilateral triangle formed by the tangent at (√3,0) to the hyperbola x^{2}−3y^{2}=3 with the pair of asymptotes of the hyperbola is
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Question 5 of 15
5. Question
3 pointsIf the circle x^{2}+y^{2}=a^{2} intersect the hyperbola xy=c^{2 }at four points (x_{i},y_{i}),and i=1,2,3,4.
Then, y_{1}+y_{2}+y_{3}+y_{4}=?
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Question 6 of 15
6. Question
3 pointsEquation of one of the tangents passing through (2,8) to the hyperbola 5x^{2}−y^{2}=5 is
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Question 7 of 15
7. Question
3 pointsA hyperbola, having the transverse axis of length 2sinθ, is confocal with the ellipse 3x^{2}+4y^{2}=12. Then its equation is
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Question 8 of 15
8. Question
3 pointsThe equation of the hyperbola which passes through the point (2,3) and has the asymptotes 4x+3y−7=0 and x−2y−1=0 is:
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Question 9 of 15
9. Question
3 pointsIf x=9 is a chord of contact of the hyperbola x^{2}−y^{2}=9, then the equation of the tangent at one of the points of contact is
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Question 10 of 15
10. Question
3 pointsThe distance between the foci of the hyperbola x^{2}−3y^{2}−4x−6y−11=0 is
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Question 11 of 15
11. Question
3 pointsLet the eccentricity of the hyperbola b^{2}x^{2}−a^{2}y^{2}=a^{2}b^{2} be reciprocal to that of the ellipse x^{2}+4y^{2}=4. If the hyperbola passes through a focus of the ellipse, then {MULTI CHOICE CORRECT}
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Question 12 of 15
12. Question
3 pointsFor the hyperbola, x^{2}sin^{2}α−y^{2}cos^{2}α= (sin^{2}α*cos^{2}α), which of the following remains constant when α varies?
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Question 13 of 15
13. Question
3 pointsIf the line ax + by + c = 0 is a normal to the hyperbola xy = 1, then
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Question 14 of 15
14. Question
3 pointsArea of triangle formed by the tangent at one vertex and asymptotes of the hyperbola xy = 2
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Question 15 of 15
15. Question
3 pointsThe product of lengths of perpendiculars from any point of the hyperbola x^{2} – y^{2} = 8 to its asymptotes is
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