Pair of Tangents from an External Point

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

1. 
2. 
3. 
4. 

Q.

Given the parabola $y^2=4ax,$ find the pair of tangents from the point (2, 6) where a =2.

1. 

2. 36x² - 4y² - 8xy + 64x + 64y + 64 =0

3. 36x² - 4y² - 48xy + 64x + 64y + 64 =0

4. 36x² - 64y² - 48xy + 64x + 64y + 64 =0

Q.

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

1. $6$
2. $6\sqrt{2}$
3. $2\sqrt{6}$
4. None

Q. Two tangents are drawn from the point $(-2,-1)$ to the parabola $y^2=4x$. If $\alpha$ is the angle between those tangents then tan $\alpha$=

1. 
2. 
3. 
4. 2

Q.

A pair of tangents are drawn from a point on the directrix to a parabola $y^2=4ax$. The angle formed by the tangents will always be ${90}^{\circ }$

1. True

2. False

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

1. True
2. False

Q. If the normals of the parabola $y^2=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x–3{)}^2+(y+2{)}^2=r^2,$ then the value of $r^2$ is

Q. Let a circle whose center on the axes touches the parabola $y^2=4x$ at two points such that pair of common tangents of the curves makes an angle of $\frac{\pi }{2}$. If the area of the circle is $k\pi$, then the value of $k$ is

Q. Let $x^2+y^2-4x-2y-11=0$ 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. If the area of the quadrilateral formed by the tangents from the origin to the circle $x^2+y^2+6x-10y+c=0$ and radii corresponding to the point of contact is $15$ sq. units, then value(s) of $c$ can be

1. $5$
2. $9$
3. $16$
4. $25$