Number of Common Tangents to Two Circles in Different Conditions
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Q. The number of common tangents to the circles x2+y2−4x−6y−12=0 and x2+y2+6x+18y+26=0 is
- 1
- 2
- 3
- 4
Q. The number of common tangents to the circles x2+y2+2x+8y−23=0 and x2+y2−4x−10y+9=0 are .
- 3
- 4
- 1
- 2
Q. For circles x2+y2+2x−8y+13=0 and x2+y2−12x−14y+76=0 equation of all the common tangents are:
- y+2=21±√5748(x+15)
- y−265=21±5√3324(x−95)
- y−265=21±5√3324(x−105)
- y−2=21±√5748(x−15)
Q.
The two circles x2+y2−4y=0 and x2+y2−8y=0
Touch each other internally
Touch each other externally
Do not touch each other
intersect each other
Q. If the circles x2+y2−2x−4y=0 and x2+y2−8y−k=0 touch each other internally, then the value of k is
- −16
- 4
- 3
- −2
Q.
Circles x2+y2−2x−4y=0 and x2+y2−8y−4=0
Touch each other internally
Cuts each other at two points
Touch each other externally
One circle lies inside the other
Q. Let the circles C1: x2+y2=9 and C2: (x−3)2+(y−4)2=16, intersect at the points X and Y. Suppose that another circle C3: (x−h)2+(y−k)2=r2 satisfies the following conditions:
(i) centre of C3 is collinear with the centres of C1 and C2.
(ii)C1 and C2 both lie inside C3, and
(iii) C3 touches C1 at M and C2 at N
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be the tangent to the parabola x2=8αy.
There are some expressions given in List−I whose values are given in List−II below:
List IList II(I)2h+k (P) 6(II)length of ZWlength of XY (Q) √6(III)Area of triangle MZNArea of triangle ZMW (R) 54(IV)α (S) 215(T) 2√6(U) 103
Which of the following is the only INCORRECT combination?
(i) centre of C3 is collinear with the centres of C1 and C2.
(ii)C1 and C2 both lie inside C3, and
(iii) C3 touches C1 at M and C2 at N
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be the tangent to the parabola x2=8αy.
There are some expressions given in List−I whose values are given in List−II below:
List IList II(I)2h+k (P) 6(II)length of ZWlength of XY (Q) √6(III)Area of triangle MZNArea of triangle ZMW (R) 54(IV)α (S) 215(T) 2√6(U) 103
Which of the following is the only INCORRECT combination?
- (I), (P)
- (IV), (U)
- (III), (R)
- (IV), (S)
Q. If two circles of radii 5 units touches each other at (1, 2) and the equation of the common tangent is 4x+3y=10, then the equation of the circle is/are
- x2+y2−10x−10y+25=0
- x2+y2+6x+2y−15=0
- x2+y2−10x−10y−25=0
- x2+y2+6x−2y+15=0
Q. If the circles x2+y2−16x−20y+164=r2 and (x−4)2+(y−7)2=36 intersect at two distinct points, then :
- 1<r<11
- 0<r<1
- r=11
- r>11
Q.
The number of common tangents to the circles x2+y2+2x+8y−23=0 and x2+y2−4x−10y+19=0 is
1
2
3
4
Q. If 3x+5y+17=0 is polar for the circle x2+y2+4x+6y+9=0, then the pole is
- (1, 2)
- (−1, 2)
- (2, 1)
- (1, −2)
Q. A circle is given by x2+(y−1)2=1, another circle C touches it externally and also the x-axis, then the locus of its centre is
- x2=2y
- x2=3y
- x2=y
- x2=4y
Q.
Let C be the circle with centre at (1, 1) and radius 1. If T is the circle centred at (0, y) passing through origin and touching the circle C externally, then the radius of T is equal to
12
14
√3√2
√32