Pair of Tangents from an External Point
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Q. Two tangents are drawn from the point (−2, −1) to the parabola y2=4x. If α is the angle between those tangents then tan α=
- 2
Q.
Tangent at a point , other than on the curve meets the curve again at . The tangent at meets the curve at and so on. Then the abscissa of , , … are in:
A.P.
G.P.
H.P.
None of these
Q. The equation to the pair of tangents drawn from (–1, –2) to parabola x2=2y is
- x2−2xy−3y2+10x+6y+9=0
- 4x2−2xy−y2+4x−6y−4=0
- x2+2xy+3y2+10x+6y+9=0
- 4x2+2xy−3y2+4x−6y−4=0
Q. Angle between the tangents drawn from the origin to the parabola y2=4a(x−a) is
- 30∘
- 45∘
- 60∘
- 90∘
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. 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
Q.
Given the parabola y2=4ax, find the pair of tangents from the point (2, 6) where a =2.
- 36x2 − 4y2 − 48xy + 64x + 64y =0
- 36x2 − 4y2 − 8xy + 64x + 64y + 64 =0
- 36x2 − 4y2 − 48xy + 64x + 64y + 64 =0
- 36x2 − 64y2 − 48xy + 64x + 64y + 64 =0
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.
A line meets the co-ordinate axes in A & B, A circle is circumscribed about the triangle OAB. If d1 and d2 are the distances of the tangent to the circle at the origin O from the points A and B respectively the diameter of the circle is:
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 sq. units.
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)