Length of intercept made by a circle on a straight line

Q.

Let $L_1$ be a straight line passing through the origin and $L_2$ be the straight line x + y = 1. If the intercepts made by

the circle $x^2+y^2-x+3y=0$ on $L_1$ and $L_2$ are equal, then which of the following equations can represent $L_1$

1. 

2. 

3. 

4. 

Q.

The circle $x^2+y^2=4$ cuts the line joining the points A(1, 0) and B(3, 4) in two points P and Q. Let $\frac{BP}{PA}=\alpha$ and

$\frac{BQ}{QA}=\beta$. Then $\alpha and\beta$ are roots of the quadratic equation

1. 

2. None of these

3. 

4. 

Q.

The area of the triangle formed by joining the origin to the points of intersection of the line $x\sqrt{5}+2y=3\sqrt{5}$ and

circle $x^2+y^2=10$ is

1. 3

2. 6

3. 4

4. 5

Q.

If the lengths of the chords intercepted by the circle $x^2+y^2+2gx+2fy=0$ from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is

1. 14

2. 13

3. 17

4. 9

Q.

The length of the chord intercepted by the circle $x^2+y^2=r^2$ on the line $\frac{x}{a}+\frac{y}{b}=1$

1. 

2. 

3. 

4.