# Angle between Pair of Tangents

## Trending Questions

**Q.**The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is 2α. The equation of the locus of the point P is

- x2+y2+4x+6y+9=0
- x2+y2−4x+6y+9=0
- x2+y2–4x–6y+9=0
- x2+y2+4x−6y+9=0

**Q.**

Two tangents are drawn from a point$P$ to the circle ${x}^{2}+{y}^{2}\xe2\u20ac\u201c2x\xe2\u20ac\u201c4y+4=0,$such that the angle between these tangents is ${\mathrm{tan}}^{-1}\left(\frac{12}{5}\right),$where ${\mathrm{tan}}^{-1}\left(\frac{12}{5}\right)\xe2\u02c6\u02c6\left(0,\mathrm{\xcf\u20ac}\right)$ If the centre of the circle is denoted by $C$and these tangents touch the circle at points $A$ and $B,$ then the ratio of the areas of $\xe2\u2013\xb3PAB$ and $\xe2\u2013\xb3CAB$ is:

$11:4$

$9:4$

$2:1$

$3:1$

**Q.**Consider the curve x2a2+y2b2=1. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of

- π4
- π3
- π2
- π6

**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, lies in

- (−1, 1)
- (1, √2)
- (−√2, −1)
- (−√2, √2)

**Q.**

The angle between the tangents drawn at the points $(5,12)$and $(12,-5)$ to the circles ${x}^{2}+{y}^{2}=169$ is

${45}^{\xc2\xb0}$

${60}^{\xc2\xb0}$

${30}^{\xc2\xb0}$

${90}^{\xc2\xb0}$

**Q.**

The cosine of the angle between the tangents from the origin to the circle x2+y2âˆ’14x+2y+25 = 0 is

1

0

-1/2

**Q.**The product of slope of tangents from point (0, 1) to the circle x2+y2−2x+4y=0 is

- −1
- 1
- −2
- 2

**Q.**The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x - 6y + 9 sin2α + 13 cos2α = 0 is 2α. The equation of the locus of the point P is

**Q.**A normal to the hyperbola, 4x2−9y2=36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the locus of P is :

- 4x2−9y2=121
- 4x2+9y2=121
- 9x2−4y2=169
- 9x2+4y2=169

**Q.**The angle between the pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13 cos2α=0 is 2α. Then the equation of the locus of the point P is

- x2+y2+4x−6y+4=0
- x2+y2+4x−6y−9=0
- x2+y2+4x−6y−4=0
- x2+y2+4x−6y+9=0

**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, lies in

- (−1, 0)∪(1, √2)
- (−1, 0)∪(√2, 5)
- (−√2, −1)∪(0, √2)
- (−√2, −1)∪(1, √2)

**Q.**Angle between tangents drawn to x2+y2−2x−4y+1=0 at the points where it is cut by the line y=2x+c, isπ2 then

- |c|=√5
- |c|=2√5
- |c|=√10
- |c|=2√10

**Q.**Common tangents are drawn to parabola y2=4x and ellipse 3x2+8y2=48 touching the parabola at A and B and the ellipse at C and D. Area of quadrilateral ABCD is ?

- 55√2 sq units
- 44√2 sq units
- 55 sq units
- 44 sq units

**Q.**Let 2x2+y2−3xy=0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 units with centre in the first quadrant. If A is one of the points of contact, then the length of OA is

- 9(1+√10) units
- 3(3+√10) units
- 9+√10 units
- 3+√10 units

**Q.**Let S be a circle whose centre is C(2, 3) and touching the y-axis. Tangents OA and OB are drawn from the origin O to the circle which touches the circle at A and B.

List IList II (A)The finite slope of the tangent OA is(P)1213(B)If α is the acute angle between the(Q)5413tangents, then the value of sinα is(C)If P(x1, y1) is any point on the circle, (R)512 then the product of the minimum and the maximum values of OP, is(D)A line is drawn from S(4, 5), intersecting (S)9the circle at M and N. Then the value of SM⋅SN is(T)4

Which of the following is the only CORRECT combination?

- (A)→(R), (B)→(P)
- (A)→(P), (B)→(R)
- (A)→(R), (B)→(S)
- (A)→(Q), (B)→(P)

**Q.**

The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is 2α. The equation of the locus of the point P is

x2+y2+4x−6y+4=0

x2+y2+4x−6y−9=0

x2+y2+4x−6y−4=0

x2+y2+4x−6y+9=0

**Q.**The slope of the normal to the curve y=2x2+3sinx at x=0 is.

- −3
- −13
- 3
- 13

**Q.**Angle between tangents drawn to x2+y2−2x−4y+1=0 at the points where it is cut by the line y=2x+c, isπ2 then

**Q.**The angle between the tangents from (α, β) to the circle x2+y2=a2, is

- None of these
- tan−1a√α2+β2−a2
- tan−1√α2+β2−a2a
- 2tan−1a√α2+β2−a2

**Q.**A point on the curve f(x)=√x2−4 defined in [2, 4] where the tangent is parallel to the chord joining two points on the curve

- (√2, √6)
- (√6, √2)
- (6, 2)
- (2, 6)

**Q.**

The angle between a pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13cos2α=0 is 2α. The equation of the locus of the point P is

x2+y2+4x−6y+4=0

x2+y2+4x−6y−4=0

x2+y2+4x−6y−9=0

x2+y2+4x−6y+9=0

**Q.**The angle between the pair of tangents drawn from a point P to the circle x2+y2+4x−6y+9sin2α+13 cos2α=0 is 2α. Then the equation of the locus of the point P is

- x2+y2+4x−6y+4=0
- x2+y2+4x−6y−9=0
- x2+y2+4x−6y−4=0
- x2+y2+4x−6y+9=0

**Q.**Let S be a circle whose centre is C(2, 3) and touching the y-axis. Tangents OA and OB are drawn from the origin O to the circle which touches the circle at A and B.

List IList II (A)The finite slope of the tangent OA is(P)1213(B)If α is the acute angle between the(Q)5413tangents, then the value of sinα is(C)If P(x1, y1) is any point on the circle, (R)512 then the product of the minimum and the maximum values of OP, is(D)A line is drawn from S(4, 5), intersecting (S)9the circle at M and N. Then the value of SM⋅SN is(T)4

Which of the following is the only CORRECT combination?

- (C)→(T), (D)→(S)
- (C)→(S), (D)→(T)
- (C)→(P), (D)→(Q)
- (C)→(P), (D)→(T)

**Q.**Find the equation of tangent and normal at t, to the curve x=asin3t, y=acos3t

**Q.**Let S be a circle whose centre is C(2, 3) and touching the y-axis. Tangents OA and OB are drawn from the origin O to the circle which touches the circle at A and B.

List IList II (A)The finite slope of the tangent OA is(P)1213(B)If α is the acute angle between the(Q)5413tangents, then the value of sinα is(C)If P(x1, y1) is any point on the circle, (R)512 then the product of the minimum and the maximum values of OP, is(D)A line is drawn from S(4, 5), intersecting (S)9the circle at M and N. Then the value of SM⋅SN is(T)4

Which of the following is the only CORRECT combination?

- (C)→(T), (D)→(S)
- (C)→(S), (D)→(T)
- (C)→(P), (D)→(T)
- (C)→(P), (D)→(Q)

**Q.**Find the equations of the tangent and normal to the given curves at the indicated points:

(i) y=x4−6x3+13x2−10x+5 at (0, 5).

(ii) y=x4−6x3+13x2−10x+5 at (1, 3)

(iii) y=x3 at (1, 1)

(iv) y=x2 at (0, 0)

(v) x=cost, y=sint at t=π4

**Q.**If the tangent at (θ) to the circle x2+y2=4 touches the circle x2+y2−6√3x−6y+20=0 then one of the values of θ is?

- π3
- π6
- π4
- π2

**Q.**Angle between tangents drawn to x2+y2−2x−4y+1=0 at the points where it is cut by the line y=2x+c, isπ2 then

- |c|=√5
- |c|=2√5
- |c|=√10
- |c|=2√10

**Q.**The angle between the two tangents from the origin to the circle (x−7)2+(y+1)2=25 is

- π3
- π6
- π2
- 0

**Q.**The angle between the tangents from a point on x2+y2+2x+4y−31=0 to the circle x2+y2+2x+4y−4=0 is

- π6
- π2
- π4
- π3