Equation of Tangent in Slope Form

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

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

Q.

A tangent PT is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3},1)$. A straight line L, perpendicular to PT is a tangent to the circle $(x-3{)}^2+y^2=1$
A possible equation of L is

1. $x-\sqrt{3}y=1$

2. $x+\sqrt{3}y=1$

3. $x-\sqrt{3}y=-1$

4. $x+\sqrt{3}y=5$

Q. A tangent PT is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3},1)$. A straight line L, perpendicular to PT is a tangent to the circle $(x-3{)}^2+y^2=1$
A common tangent of the two circles is

1. $x=4$
2. $y=2$
3. $x+\sqrt{3}y=4$
4. $x+2\sqrt{2}y=6$

Q. The line lx + my + n = 0 will be a tangent to the circle $x^2+y^2=a^2$ iff

1. n(l + m) = a
2. a(l + m) = n
3. $n^2(l^2+m^2)=a^2$
4. $a^2(l^2+m^2)=n^2$

Q. Let $P$ be a point on the parabola, $x^2=4y$. If the distance of $P$ from the centre of the circle, $x^2+y^2+6x+8=0$ is minimum, then the equation of the tangent to the parabola at $P$, is

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

Q. If the dimensions of the triangle PQR are as given, then find the set of possible coordinates of the points P, Q and R.

1. P(2, 2); Q(2, 5); R(6, 2)
2. P(3, 3); Q(3, 5); R(6, 3)
3. P(3, 3); Q(3, 6); R(6, 3)
4. P(2, 2); Q(5, 2); R(6, 2)

Q. There are 2 △s ABC and A'B'C'. The plotting for △ABC with vertices (0, 3), (5, 0), and (5, 6) and △A'B'C' with (1, 3), (4, 1), and (4, 5) is

1. False
2. True