## 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 ?CorrectIncorrect - 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 toCorrectIncorrect - 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 x-axis and y-axis at A and B respectively. Then (OA)^{2}−(OB)^{2}, where O is the origin, equals:CorrectIncorrect - 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 isCorrectIncorrect - 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}=?CorrectIncorrect - 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 isCorrectIncorrect - 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 isCorrectIncorrect - 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:

CorrectIncorrect - 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 isCorrectIncorrect - Question 10 of 15
##### 10. Question

3 pointsThe distance between the foci of the hyperbola x

^{2}−3y^{2}−4x−6y−11=0 isCorrectIncorrect - 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}**CorrectIncorrect - 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?CorrectIncorrect - Question 13 of 15
##### 13. Question

3 pointsIf the line ax + by + c = 0 is a normal to the hyperbola xy = 1, then

CorrectIncorrect - Question 14 of 15
##### 14. Question

3 pointsArea of triangle formed by the tangent at one vertex and asymptotes of the hyperbola xy = 2

CorrectIncorrect - 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 isCorrectIncorrect