Tangent

Q. If a circle whose centre is (1, –3) touches the line 3x – 4y –5 = 0, then the radius of the circle is

1. 2
2. 
3. 
4. 4

Q. The equation of the circle passing through the point (1, –2) and having its centre on the line 2x – y – 14 = 0 and touching the line 4x + 3y – 23 = 0

1. + + 8x + 12y + 27 = 0
2. + - 8x + 12y + 27 = 0
3. + - 12y + 27 = 0
4. + - 8x + 12y + 27 = 0

Q. If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is

1. 3/2
2. 3/4
3. 1/10
4. 1/20

Q. The equation of circle with centre (1, 2) and tangent x + y - 5 = 0 is

1. $x^2+y^2-2x-4y+3=0$
2. $x^2+y^2+2x-4y+6=0$
3. $x^2+y^2-2x-4y+8=0$
4. $x^2+y^2-2x+4y+8=0$

Q. The two tangents to a circle from an external point are always

1. None of these

2. Equal

3. Perpendicular to each other

4. Parallel to each other

Q. If the line lx + my = 1 be a tangent to the circle $x^2+y^2=a^2,$ then the locus of the point (l, m) is

1. A straight line

2. An ellipse

3. A Circle

4. A parabola

Q. The equation to the circle with centre (2, 1) and touching the line 3x + 4y = 5 is

1. $x^2+y^2-4x-2y+5=0$
2. $x^2+y^2-4x-2y-5=0$
3. $x^2+y^2-4x-2y+4=0$
4. $x^2+y^2-4x-2y-4=0$

Q. The equation of circle which touches the axes of coordinates and the line $fracx3+\frac{y}{4}$ and whose centre lies in the first quadrant is $x^2+y^2-2cx-2cy+c^2=0,$ where c is

1. 3
2. 6
3. 1
4. 2

Q.

The perpendicular distance of center from tangent of the circle is equal to its radius.

1. True

2. False

Q.

The foot of the perpendicular of center on a tangent and the point of contact of the tangent are same.

1. True

2. False