Intercept Made by Circle on Axes

Q. The length of intercept, the circle $x^2+y^2+10x-6y+9=0$ makes on the x-axis is

1. 8
2. 2
3. 4
4. 6

Q.

The lengths of the intercepts made by any circle on the coordinates axes are equal if the centre lies on the line (s) represented by

1. x+y+1=0
   

2. x+y=1
   

3. x-y=1

4. $x^2-y^2=0$
   

Q. The equation of a circle which touches both axes and the line 3x - 4y + 8 =0 and whose centre lies in the third quadrant is

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

Q. Which of the following is/are true for the eqaution $ax+by+c=0$?

(More than one correct answer)

1. If a=0, the line is parallel to y-axis
2. If a=0, the line is parallel to x-axis
3. If b=0, the line is parallel to y-axis
4. If b=0, the line is parallel to x-axis

Q. The circle $x^2+y^2+4x-4y+4=0$ touches

1. x-axis

2. y-axis

3. x-axis and y-axis
4. None of these

Q. A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. The radius of the circle is

1. 4
2. 5
3. 3
4. 6

Q. lf $g^2<c<f^2$ then the circle $x^2+y^2+2gx+2fy+c=0$ intersects

1. the coordinate axes
2. the y - axis but not the x- axis
3. the x - axis but not the y - axis
4. None of these

Q.

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point

1. $[\frac{2a{b}^2}{a^2+b^2},\frac{2a^{2}b}{a^2+b^2}]$
   

2. $[\frac{2a^{2}b}{a^2+b^2},\frac{2a{b}^2}{a^2+b^2}]$
   

3. $[\frac{2ab}{a^2+b^2},\frac{2ab}{a^2+b^2}]$
   

4. $(a,b)$
   

Q.

A triangle is formed by the line 3x + 4y = 12, the x-axis and y-axis. The circumradius is

1. 2.5

2. 3

3. 5

4. 4