Pair of Tangents from an External Point
Q. The equation to the pair of tangents drawn from (–1, –2) to parabola x2=2y is
Given the parabola y2=4ax, find the pair of tangents from the point (2, 6) where a =2.
36x2 - 4y2 - 8xy + 64x + 64y + 64 =0
36x2 - 4y2 - 48xy + 64x + 64y + 64 =0
36x2 - 64y2 - 48xy + 64x + 64y + 64 =0
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
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=
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∘
Q. The tangents at the exterimities of any focal chord of a parabola intersect at right angle at the directrix.
Q. If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x–3)2+(y+2)2=r2, then the value of r2 is
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. 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. 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