Definition of Hyperbola
Trending Questions
Q. The equation of hyperbola whose axes are the coordinates axes, one vertex is (−3, 0) and eccentricity is √52 is
x29−2y227=1
- x29−y227=1
- x215−y226=1
- x29−3y227=1
Q. If two circles are given such that they neither intersect nor touches each other. Then the locus of centre of variable circle which touches both the circles externally is
- circle
- parabola
- ellipse
- hyperbola
Q. The eccentricity of the hyperbola whose length of latus rectum is half the length of transverse axis is
- √32
- 32
- 2
- 83
Q. Which of the following equation(s) (t being the parameter) represents a hyperbola?
- txa−yb+t=0, xa+tyb−1=0
- x=a2(t+1t), y=b2(t−1t)
- x=et+e−t, y=et−e−t
- x2=2(cost+3), y2=2(cos2t2−1)
Q.
An equation x2p + y2q = 1 represents a hyperbola is p and q are of the opposite signs.
True
False
Q.
If P is a point on the rectangular hyperbola x2−y2=a2, C is its centre and S, S′ are the two foci, the SP⋅S′P=
2
(CP)2
(CS)2
(SS′)2
Q.
The equation x212−k + y28−k = 1 represents.
A hyperbola, if k < 8
A ellipse, if k > 8
A hyperbola, if 8 < k < 12
None of the above
Q. The equation of asymptotes for a conjugate hyperbola are obtained by multiplying the equations of asymptotes of standard hyperbola by −1
- True
- False
Q. The exhaustive set of values of a2 such that there exists a tangent to the ellipse x2+a2y2=a2 such that the portion of the tangent intercepted by the hyperbola a2x2−y2=1 subtends a right angle at the origin.
- [√5+12, 2]
- (1, 2]
- [√5−12, 1)
- [√5−12, 1)∪(1, √5+12]
Q. Let the eccentricity of the hyperbola x2a2−y2b2=1 be the reciprocal to that of the ellipse x2+4y2=4. If the hyperbola passes through the focus of the ellipse, then the focus of the hyperbola is at :
- (2, 0)
- (0, 2)
- (3, 0)
- (0, 3)
Q. If e1 and e2 are the eccentricities of the ellipse, x218+y24=1 and the hyperbola, x29−y24=1 respectively and (e1, e2) is a point on the ellipse, 15x2+3y2=k. Then k is equal to
- 14
- 15
- 17
- 16