Length of External Common Tangent

Q.

Find common tangent of the two curves $y^2=4x$ and $x^2+y^2-6x=0$.

1. $y=\frac{x}{3}+3$

2. $y=\frac{x}{\sqrt{3}}-\sqrt{3}$

3. $y=\frac{x}{3}-3$

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

Q. The radius is parallel to the tangent at the point of contact.

1. True
2. False

Q.

If one circle lie completely outside the other circle, Q , the intersection of direct common tangent, lie on the line joining the centers of the two circles and divide it internally in the ratio of their radii.

1. True

2. False

Q.

Find the length of direct common tangent for circles $x^2+y^2-20x+64=0$and $x^2+y^2+30x+144=0$

1. $2\sqrt{150}$

2. $2\sqrt{154}$

3. 9

4. 20

Q.

P and Q are the centres of two circles whose radii are 5 cm and 11 cm, respectively. If the direct common tangent to the circles meets PQ at M, then, M divides PQ in the ratio ___

1. 5 : 11 internally

2. 11 : 5 internally

3. 5 : 11 externally

4. 11 : 5 externally

Q.

P and Q are the centres of two circles whose radii are 5 cm and 11 cm, respectively. If the direct common tangent to the circles meets PQ at M, then, M divides PQ in the ratio ___

1. 5 : 11 internally

2. 11 : 5 internally

3. 5 : 11 externally

4. 11 : 5 externally