Pair of Tangents from a Point
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Q. The equations of the tangents drawn from the point (0, 1) to the circle x2+y2−2x+4y=0 are
- 2x - y + 1 = 0, x + 2y - 2 = 0
- 2x - y + 1 = 0, x + 2y - 2 = 0
- 2x - y - 1 = 0, x + 2y - 2 = 0
- 2x - y - 1 = 0, x + 2y + 2 = 0
Q.
The length (in units) of the tangent from point to the circle is
Q. The equation of pair of tangents drawn to the circle x2+y2−2x+4y+3=0 from point (6, −5) is
- 7x2+23y2+30xy+66x+50y−73=0
- 7x2+23y2−30xy+66x−50y−73=0
- 7x2+3y2+30xy−66x+50y−73=0
- 3x2+7y2+30xy+66x+50y−73=0
Q.
A circle is of the form x2 + y2 + 2gx + 2fy + c = 0 and a pair of tangents are drawn from (x1, y1) to the circle.The combined equation of tangents is SS1 = T2.
Where S=x2+y2+2gx+2fy+c
S1=x21+y21+2gx1+2fy1+c
T=xx1+yy1+g(x+x1)+f(y+y1)+c
True
False
Q. An infinite number of tangents can be drawn from (1, 2) to the circle x2+y2−2x−4y+λ=0. Then λ is
- −20
- Not possible
- 5
- 20
Q. P is a variable point on the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQRS is completed.
If P≡(3, 4), then coordinate of S is
If P≡(3, 4), then coordinate of S is
- (−4625, −6325)
- (−5125, −6825)
- (−4625, −6825)
- (−6825, −5125)
Q. Let A be the centre of the circle x2+y2 - 2x - 4y - 20 = 0. Suppose that the tangents at the points B(1, 7) and D(4, - 2) on the circle meet at the point C. The area of the quadrilateral ABCD is
- 75 sq. unit
- 145 sq. unit
- 150 sq. unit
- 50 sq. unit
Q. Tangents drawn from the point P(1, 8) to the circle x2+y2−6x−4y−11=0 touch the circle at points A and B. The equation of the circumcircle of triangle PAB is
- x2+y2+4x−6y+19=0
- x2+y2−4x−10y+19=0
- x2+y2−2x+6y−20=0
- x2+y2−6x−4y+19=0
Q. P is a variable point on the line L=0. Tangents are drawn to the circle x2+y2=4 from P to touch it at Q and R. The parallelogram PQRS is completed.
If P≡(6, 8), then the area of △QRS is
If P≡(6, 8), then the area of △QRS is
- 196√525 sq. unit
- 196√652 sq. unit
- 192√625 sq. unit
- 196√525 sq. unit
Q. An infinite number of tangents can be drawn from (1, 2) to the circle x2+y2−2x−4y+λ=0. Then
- λ=20
- λ=−20
- λ=5
- no such λ exists
Q. If O is the origin and OP, OQ are the tangents from the origin to the circle x2+y2−6x+4y+8=0, the circumcenter of the triangle OPQ is
- (3, −2)
- (32, −1)
- (34, −12)
- (−32, 1)
Q. Let the point B be the reflection of the point A(2, 3) with respect to the line 8x−6y−23=0. Let ΓA and ΓB be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles ΓA and ΓB such that both the circles are on the same side of T. If C is the point of intersection of T and line passing through A and B, then the length of the line segment AC is
Q.
The range of values of 'a' such that the angle θ between the pair of tangents drawn from (a, 0) to the circle x2+y2=1 satisfies π2<θ<π, is
(1, 2)
(1, √2)
(−√2, −1)
(−√2, −1)∪(1, √2)
Q. The locus of the point of intersection of two perpendicular tangents to the circle x2+y2=a2 is
- x2+y2=a22
- x2+y2=a23
- x2+y2=2a2
- x2+y2=3a2
Q. Let x2+y2−4x−2y−11=0 be a circle. A pair of tangents from the point (4, 5) with a pair of radii form a quadrilateral of area ___ .
Q. A pair of tangents is drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of 60∘. The area enclosed by these tangents and the arc of the circle is
- 2√3−π6 sq. units
- √3−π3 sq. units
- π3−√36 sq. units
- √3(1−π6) sq. units