# Pair of Tangents from an External Point

## Trending Questions

**Q.**Angle between the tangents drawn from the origin to the parabola y2=4a(x−a) is

- 30∘
- 45∘
- 60∘
- 90∘

**Q.**Let the tangent to the parabola S:y2=2x at the point P(2, 2) meet the x−axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to

- 252
- 152
- 352
- 25

**Q.**PG is the normal at P to the parabola y2=4ax. G is on the axis, GP is produced to Q such that PQ=GP, then

- Locus of Q is y2=16a(x+2a)
- Focus of locus of Q is (2a, 0)
- Latus rectum of locus of Q is 16a
- Locus of Q is y2=16a(x−2a)

**Q.**The length of the chord of the parabola x2=4y having equation x−√2y+4√2=0 is :

- 3√2
- 2√11
- 6√3
- 8√2

**Q.**

Find the equation of the tangent line to the curve y=x2−2x+7 which is

(a) parallel to the line 2x-y+9=0.

(a) parallel to the line 5y-15x=13.

**Q.**Suppose that the foci of the ellipse x29+y25=1 are (f1, 0) and (f2, 0) where f1>0 and f2<0. Let P1 and P2 be two parabolas with a common vertex at (0, 0) and with foci at (f1, 0) and (2f2, 0), respectively. Let T1 be a tangent to P1 which passes through (2f2, 0) and T2 be a tangent to P2 which passes through (f1, 0). If m1 is the slope of T1 and m2 is the slope of T2, then the value of (1m21+m22) is

**Q.**

Tangents are drawn from the point (−1, 2) to the parabola y2=4x. The length of the intercept made by the line x=2 on these tangents is

- 6
- 6√2
- 2√6
- None

**Q.**If the locus of mid point of the chords of the parabola y2=4ax which passes through a fixed point (h, k) is also a parabola, then length of its latus rectum (in units) is

- 4a
- 8a
- 6a
- 2a

**Q.**If two tangents drawn from the point (α, β) to the parabola y2=4x such that the slope of one tangent is double of the other, then

- β=29α2
- α=29β2
- 2α=9β2
- α=2β2

**Q.**If the tangents at P and Q on the parabola y2=4ax meets at T and if S is the focus of the parabola then, SP, ST, SQ are in

- A.P.
- G.P.
- H.P
- A.G.P.

**Q.**If the locus of mid point of any normal chord of the parabola y2=4x is x−a=by2+y2c; where a, b, c∈N, then (a+b+c) is equal to

**Q.**If the area of the quadrilateral formed by the tangents from the origin to the circle x2+y2+6x−10y+c=0 and radii corresponding to the point of contact is 15 sq. units, then value(s) of c can be

- 5
- 9
- 16
- 25

**Q.**Consider the hyperbola H: x2−y2=1 and a circle S with center N(x2, 0). Suppose that H and S touch each other at a point P(x1, y1) with x1>1 and y1>0. The common tangent to H and S at P intersects the x−axis at point M. If (l, m) is the centroid of the triangle △PMN, then the correct expression(s) is (are)

- dldx1=1−13x21 for x1>1
- dmdx1=x13(√x21−1) for x1>1
- dldx1=1+13x21 for x1>1
- dmdy1=13 for y1>1

**Q.**Equation(s) of the tangents drawn from (4, 10) to the parabola y2=9x is/are

- x−4y+36=0
- 9x−4y+4=0
- x−2y+4=0
- x−y+1=0

**Q.**The area of the triangle formed by any tangent to the hyperbola x2a2−y2b2=1 with its asymptotes is

**Q.**If θ is the angle between the two tangents to y2=12x drawn from the point (1, 4), then tanθ is equal to

- 23
- 35
- 12
- 34

**Q.**

Number of points from where perpendicular tangents to the curve x216−y225=1 can be drawn, is:

2

1

3

0

**Q.**The base of triangle is divided into three equal parts. If t1, t2, t3 be the tangents of the angle subtended by these parts at the opposite vertices. The relationship between t1, t2, t3 is given by the following equation

(1t1+1t2)(1t2+1t3)=k(1+1t22). Then the value of k is

**Q.**The tangent & Normal at any point P of the parabola intersect the axis at T & G. Centre of the circle circumscribing triangle PTG is the vertex of the parabola.

True

False

**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 are drawn from a point on the directrix to a parabola y2=4ax. The angle formed by the tangents will always be 90∘

True

False

**Q.**If the tangents are drawn at (at21, 2at1) and (at22, 2at2) on the parabola y2=4ax intersect on axis of the parabola, then

- t1t2=2
- t1=−t2
- t1t2=−1
- t1t2=−4

**Q.**The equation to the pair of tangents drawn from (–1, –2) to parabola x2=2y is

**Q.**

If OA and OB are two equal chords of the circle x2+y2−2x+4y=0 perpendicular to each passing through the origin O, the slopes of OA and OB are the roots of the equation

**Q.**PG is the normal at P to the parabola y2=4ax. G is on the axis, GP is produced to Q such that PQ=GP, then

- Locus of Q is y2=16a(x+2a)
- Focus of locus of Q is (2a, 0)
- Latus rectum of locus of Q is 16a
- Locus of Q is y2=16a(x−2a)

**Q.**The tangents at the exterimities of any focal chord of a parabola intersect at right angle at the directrix.

- True
- False

**Q.**One of the sides of a triangle is divided into segments of 4 and 6 units by the point of tangency of the inscribed circle which has radius 2√2 units, then the largest side of triangle is -

- 10
- 212
- 434
- 11

**Q.**Let a circle whose center on the axes touches the parabola y2=4x at two points such that pair of common tangents of the curves makes an angle of π2. If the area of the circle is kπ, then the value of k is

**Q.**Find the shortest distance of the point (0, c) from the parabola y=x2, where c>0

**Q.**Let the tangents from P are drawn to a circle with centre C such that PC=2 units. If equation of the tangents are x2=3y2, then radius of the circle can be

- √2 unit
- √3 unit
- 2 unit
- 1 unit