Length of Intercept Made by a Circle on a Straight Line

Q. The range of values of m for which the line y = mx + 2 cuts the circle $x^2+y^2=1$ at two distinct points, is .

1. $m\in (-\infty ,-\sqrt{3})\cup (\sqrt{3},\infty )$
2. $m\in (-\infty ,-\sqrt{3})$
3. $m\in (\sqrt{3},\infty )$
4. $m\in (-\sqrt{3},\sqrt{3})$

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. 17

2. 9

3. 14

4. 13

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. 4

2. 3

3. 5

4. 6

Q. If 3x – 4y + 12 = 0 and 3x + 2y – 6 = 0, then area of triangle formed by the given lines and x-axis is (in sq. units)

Q. Let a circle be given by $2x(x-a)+y(2y-b)=0;$ $(a\ne 0,b\ne 0)$.

1. $2a^2<b^2$
2. $a^2<2b^2$
3. $a^2>2b^2$
4. $2a^2>b^2$