Position of a Point W.R.T Parabola
Trending Questions
Q. If (α2, α−2) be a point interior to the regions of the parabola y2=2x bounded by the chord joining the points (2, 2) and (8, −4), then α belongs to the interval
- −2+2√2<α<2
- α>−2+2√2
- α>−2−2√2
- α<−2−2√2
Q. Let the curve C be the mirror image of the parabola y2=4x with respect to the line x+y+4=0. If A and B are the points of intersection of C with the line y=–5, then the distance between A and B is
Q. the vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foci is at (18, 0) the equation of hyperbola is
Q. The number of points with non-negative integral coordinates that lie in the interior of the region common to the circle x2+y2=16 and the parabola y2=4x, is
- 4
- 8
- 10
- 12
Q. The point (-1, 7) does not lie inside the parabola y2 = 12x.
- False
- True
Q. The number of points with non-negative integral coordinates that lie in the interior of the region common to the circle x2+y2=16 and the parabola y2=4x, is
Q. The equation of a parabola is y2=4x. Let P (1, 3) and Q (1, 1) are two points in the xy plane. Then,
- P and Q are exterior points
- P is an interior point while Q is an exterior point
- P and Q are interior points
- P is an exterior point while Q is an interior point
Q. The point (−2m, m+1) is an interior point of the smaller region bounded by the circle x2+y2=4 and the parabola y2=4x, then m lies in the interval
- −5−2√6<m<1
- 0<m<4
- −1<m<35
- −1<m<−5+2√6
Q.
The range of λ if the point (λ, λ+1) lies inside the parabola y2=14x
(12−√1402, 12+√1402)
(14−√1902, 14+√1902)
(6, 8)
(12−√1402, 14+√1902)
Q. If point (k, k+2) lies inside the region bounded by parabolas x2=4(y+2) and x2=−(y−4) in first quadrant, then k lies in the interval
- (0, 2+2√5)
- (−2, 0)
- (0, 1)
- (2−2√5, 2+2√5)
Q. The image of the point (3, 5) in the line x–y+1=0, lies on :
- (x−4)2+(y−4)2=8
- (x−2)2+(y−4)2=4
- (x−2)2+(y−2)2=12
- (x−4)2+(y+2)2=16
Q. If point (k, k2) lies inside the region bounded by parabolas y2=64x and −x2+x−1+y=0 then k lies in the interval
- k∈(1, 4)
- k∈(0, 4)
- k∈(1, ∞)
- k∈(−∞, 4)
Q. In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is
(a)
(b)
(c)
(d) none of these
(a)
(b)
(c)
(d) none of these