Length of Internal Common Tangent

Q. The length of transverse common tangent to two circles is $5\text{units}$ and a direct common tangent is $15\text{units}$, then the product of the radii of two circles is

1. $25$
2. $50$
3. $75$
4. $30$

Q.

If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) 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. The length of transverse common tangent to two circles is $5\text{units}$ and a direct common tangent is $15\text{units}$, then the product of the radii of two circles is

1. $25$
2. $50$
3. $75$
4. $30$

Q.

Length of internal (transverse) common tangent to two circles is $L_{int}=\sqrt{d^2-(r_1-r_2{)}^2}$

Where d = distance between the centers of the two circles $r_1\&r_2$ are radii of two circles

1. True

2. False

Q. $\text{If line}y=2x+\frac{1}{4}\text{is tangent to}$
$y^2=4ax\text{then}a\text{is equal to}$

1. $\frac{1}{2}$
2. $2$
3. $1$
4. None of the above

Q.

Length of internal (transverse) common tangent to two circles is $L_{int}=\sqrt{d^2-(r_1-r_2{)}^2}$

Where d = distance between the centers of the two circles $r_1\&r_2$ are radii of two circles

1. True

2. False

Q. If the tangent to the curve $y=e^x$ at a point $(c,e^c)$ and the normal to the parabola $y^2=4x$ at the point $(1,2)$ intersect at the same point on the $x$-axis, then the value of $c$ is

Q.

If one circle lie completely outside the other circle, P, the intersection of transverse (indirect) 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.

Length of internal (transverse) common tangent to two circles is $L_{int}=\sqrt{d^2-(r_1-r_2{)}^2}$

Where d = distance between the centers of the two circles $r_1\&r_2$ are radii of two circles

1. True

2. False