Pair of Tangents from a Point

Q. Let A be the centre of the circle $x^2+y^2$ - 2x - 4y - 20 = 0. Suppose that the tangents at the points B(1, 7) and D(4, - 2) on the circle meet at the point C. The area of the quadrilateral ABCD is

1. 75 sq. unit
2. 145 sq. unit
3. 150 sq. unit
4. 50 sq. unit

Q.

If $\theta$ is in the first quadrant, then $\sqrt{(1-sin2\theta )}$ = - cos$\theta$

1. True

2. False

Q. The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4x-5y=20$ to the circle $x^2+y^2=9$ is

1. $20(x^2+y^2)-36x+45y=0$
2. $20(x^2+y^2)+36x-45y=0$
3. $36(x^2+y^2)-20y+45y=0$
4. $36(x^2+y^2)+20x-5y=0$

Q. The equations of the tangents drawn from the origin to the circle $x^2+y^2-2rx-2hy+h^2=0$ are

1. $(h^2-r^2)x+2rhy=0,x=0$
2. x = 0, y = 0
3. $(h^2-r^2)x-2rhy=0,x=0$
4. y = 0, x = 4

Q. Find the equation of tangent at $(3,4)$ for the circle $x^2+y^2=25$

1. $4x-3y=25$
2. $3x+4y=25$
3. $3x-4y=25$
4. $3x+4y+25=0$

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 ___.