Position of a Point with Respect to Circle
Trending Questions
Q. A point inside the circle x2+y2+3x−3y+2=0 is
- (-1, 3)
- (-2, 1)
- (2, 1)
- (-3, 2)
Q.
If the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinates axes in concyclic points, then
- a1b1=a2b2
- a1a2=b1b2
- a1+a2=b1+b2
- a1a2=b1b2
Q. The number of tangents which can be drawn from the point (–1, 2) to the circle x2+y2+2x−4y+4=0 is
- 1
- 2
- 3
- \N
Q.
What is the maximum and minimum distance of the point (9, 12) from the circle x2+y2−6x−8y−24=0
15 and 5
14 and 6
12 and 8
17 and 3
Q. If (a, 0) is an endpoint of a diameter of the circle x2+y2=4, then x2−4x−a2=0 has
- exactly one real root in (−1, 0]
- exactly one real root in [2, 5]
- distinct roots greater than −1
- distinct roots less than 5
Q. If P(2, 8) is an interior point of a circle x2+y2−2x+4y−p=0 which neither touches nor intersects the axes, then set for p is -
- p<−1
- p<−4
- p>96
- p∈ϕ
Q. For the circle x2+y2+6x+8y=0, and the points P(−3, −6) and Q(4, −2),
- P, Q lie inside the circle
- P, Q lie outside the circle
- P lies inside and Q lies outside the circle
- Q lies inside and P lies outside the circle
Q. Consider the relation 4l2−5m2+6l+1=0, where l, m∈R, then the line lx+my+1=0 touches a fixed circle whose number of tangents which can be drawn from the point (2, −3) are
- 0
- 1
- 2
- 1 or 2
Q. If the straight line xcosθ+ysinθ=2 touches the circle x2+y2−2x=0 then
- θ=nπ, n∈Z
- θ=(2n+1)π, n∈Z
- θ=2nπ, n∈Z
- θ=(2n+1)π2, n∈Z
Q. The range of values of α for which the point (α, α) lies in the interior part of smaller segment of x2+y2=4 intercepted by the line 3x+4y+7=0, is
- (−∞, √2)
- (−√2, √2)
- (−√2, −1)
- ϕ
Q.
The point P(9, 12) lies inside the circle x2+y2−6x−8y−24=0
True
False
Q. From the point P(2, 1), a line of slope m∈R is drawn so as to cut the circle x2+y2=1 in points A and B. If the slope m is varied, then the greatest possible value of PA+PB is
- 2√5
- 10√5
- 2√5
- 1√5
Q. Consider the relation 4l2−5m2+6l+1=0, where l, m∈R, then the line lx+my+1=0 touches a fixed circle whose number of tangents which can be drawn from the point (2, −3) are
- 0
- 1
- 2
- 1 or 2
Q. The greatest distance of the point P(9, 7), from the circle x2+y2−2x−2y−23=0, is units
Q. The point (1, 2) lies outside the circle x2+y2−4x+2y−11=0.
- False
- True
Q.
The power of (2, 1) with respect to the circle 2x2+2y2−8x−6y+k = 0 is positive if
0<k<12
-12<k<12
k>12
k<12
Q. The nearest point on the circle x2+y2−6x+4y−12=0 from the point P(−5, 4) is Q(α, β), then the value of α+β is
- 0
- 4
- 2
- 7
Q. The range of parameter a for which the variable line y=2x+a lies between the circles x2+y2−2x−2y+1=0 and x2+y2−16x−2y+61=0 without intersecting or touching either circle is
- (−15, −1)
- (−∞, −2√5−15)
- (2√5−15, −√5−1)
- (√5−1, ∞)
Q. Let C:x2+y2−x−y−6=0 and point P(a−1, a+1) lies inside the circle C. If the line x+y−2=0 divides the circle in two segments, then
- P to lie in the larger segment of the intersection if a∈(−1, 1)
- P to lie in the larger segment of the intersection if a∈(1, 2)
- P to lie in the smaller segment of the intersection if a∈(1, 2)
- P to lie in the smaller segment of the intersection if a∈(−1, 1)