Intercept Made by Circle on Axes

Q. If a circle of constant radius 3k passes through the origin ‘O’ and meets co-ordinate axes at A and B then the locus of the centroid of the triangle OAB is

1. $x^2+y^2=(2k{)}^2$
2. $x^2+y^2=(3k{)}^2$
3. $x^2+y^2=(4k{)}^2$
4. $x^2+y^2=(6k{)}^2$

Q. The midpoint of line segment joining A(2, 3) and B(4, 5) lies on the curve.

1. $x+y=5$
2. $x^2+y^2=25$
3. $x+2y=8$

Q.

The circles ${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}-4\mathrm{y}+4=0$ touches

1. $X-$axis

2. $Y-$axis

3. $X-$axis and $Y-$axis

4. None of these

Q. The length of X and Y intercepts made by the circle $x^2+y^2-10x+6y+9=0$ is and respectively.

1. \N
2. 2
3. 4
4. 8

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. Radius of circle touching y-axis at point $P(0,2)$ and circle $x^2+y^2=16$ internally-

1. $\frac{3}{2}$
2. $\frac{5}{4}$
3. $2$
4. $\frac{5}{2}$

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

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

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

4. $(a,b)$
   

Q. Locus of mid-points of all chords of the parabola $y^2=4x$ which are drawn through the vertex is

1. $y^2=8x$
2. $y^2=2x$
3. $x^2+4y^2=16$
4. $x^2=2y$

Q. A circle is given by $x^2+(y-1{)}^2=1.$ Then the locus of the centre of the circle touching the given circle and the $x$-axis, is

1. $\left\{\right(x,y)|x^2=4y\}\cup \left\{\right(x,y)|y\le 0\}$
2. $\left\{\right(x,y)|x^2+(y-1{)}^2=4\}\cup \left\{\right(x,y)|y\le 0\}$
3. $\left\{\right(x,y)|x^2=4y\}$
4. $\left\{\right(x,y)|x^2=4y\}\cup \left\{\right(0,y)|y\le 0\}$

Q. Consider a family of circle which are passing through the point $(-1,1)$ and are tangent to x-axis. If $(h,k)$ are the co-ordinates of the centre of the circles, then the set of values of $k$ is given by the interval

1. $k\ge \frac{1}{2}$
2. $-1\frac{1}{2}\le k\le \frac{1}{2}$
3. $k\le \frac{1}{2}$
4. $0<k<\frac{1}{2}$