Equation of Tangent in Slope Form

Q. The equations of the tangents to the circle $x^2+y^2$ - 4x - 6y - 12 = 0 and parallel to 4x - 3y = 1 are

1. 4x + 3y + 14 = 0, 4x + 3y + 16 = 0
2. 4x – 3y – 24 = 0, 4x – 3y + 26 = 0
3. x – y – 14 = 0, x – y + 16 = 0
4. 4x – 3y + 34 = 0, 4x – 3y + 16 = 0

Q. Let tangents are drawn at two points of the circle $(x-7{)}^2+(y+1{)}^2=25$. If the point of intersection of both the tangents is origin, then the angle between them (in degrees) is

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

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

Q. The equations of the tangents to the circle $x^2+y^2-6x+4y=12$ which are parallel to the straight line 4x + 3y + 5 = 0, are

1. 3x - 4y + 19 = 0, 3x - 4y + 31 = 0
2. 3x - 4y - 19 = 0, 3x - 4y + 31 = 0
3. 4x + 3y - 19 = 0, 4x + 3y + 31 = 0
4. 4x + 3y + 19 = 0, 4x + 3y - 31 = 0

Q.

The equation of tangent with slope m of the circle $x^2+y^2=a^2$ are given by $y=mx\pm m\sqrt{1+a^2}$

1. True

2. False

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. Equation of a common tangent to the circle, $x^2+y^2-6x=0$ and the parabola, $y^2=4x$, is

1. $2\sqrt{3}y=-x-12$
2. $2\sqrt{3}y=12x+1$
3. $\sqrt{3}y=x+3$
4. $\sqrt{3}y=3x+1$

Q. The area (in sq. units) of the smaller of the two circles that touch the parabola, $y^2=4x$ at the point $(1,2)$ and the $x$-axis is :

1. $4\pi (3+\sqrt{2})$
2. $8\pi (2-\sqrt{2})$
3. $8\pi (3-2\sqrt{2})$
4. $4\pi (2-\sqrt{2})$