Intercept Made by Circle on Axes

Q. A circle touching the $x$-axis at $(3,0)$ and making an intercept of length $8$ on the $y$-axis passes through the point :

1. $(3,10)$
2. $(3,5)$
3. $(1,5)$
4. $(2,3)$

Q. Consider the circle $|z-5i|=3$ and two points $z_1$ and $z_2$ on it such that $|z_1|<|z_2|$ and $\arg \left(z_1\right)=\arg \left(z_2\right)=\frac{\pi }{3}.$ A tangent is drawn at $z_2$ to the circle, which cuts the real axis at $z_3,$ then $|z_3|$ is

1. $3$
2. $\sqrt{13}$
3. $4$
4. $\sqrt{11}$

Q. A circle cuts a chord of length $4a$ on the $x$-axis and passes through a point on the $y$-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is :

1. a straight line
2. an ellipse
3. a parabola
4. a hyperbola

Q. The circle $x^2+y^2-8x+4y+4=0$ touches

1. x-axis only

2. y- axis only

3. Both x and y- axis
4. Does not touch any axis

Q. For how many values of $p$, the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points? .
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Q. Let a circle is touching exactly two sides of a square $ABCD$ and passes through exactly one of its vertices. If area of the square $ABCD$ is $1$ sq. units, then the radius of the circle (in units) is

1. $2-\sqrt{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\sqrt{2}-1$
4. $\frac{1}{2}$

Q.

The equation of the circle in the first quadrant which touches each axis at a distance 5 from the origin is

1. $x^2+y^2+10x+10y+25=0$

2. $x^2+y^2+5x+5y+25=0$

3. $x^2+y^2-5x-5y+25=0$

4. $x^2+y^2-10x-10y+25=0$

Q. The circle $x^2+y^2-3x-4y+2=0$ cuts x-axis at

1. (1, 0), (2, 0)
2. (2, 0), (-3, 0)
3. (1, 0), (-1, 0)
4. (3, 0), (4, 0)

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

Q.

If the centroid of an equilateral triangle is $(1,1)$and its one vertex is $(-1,2)$, then the equation of its circumcircle is:

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

2. ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}-2\mathrm{y}-3=0$

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

4. none of these

Q. If $(h,k)$ is the centre of a circle touching $x-$axis at a distance $3$ units from the origin and makes an intercept of $8$ units on the $y-$axis, then the equation of circle when $(h+k)$ is maximum, is

1. $(x-5{)}^2+(y-3{)}^2=25$
2. $(x+5{)}^2+(y+3{)}^2=25$
3. $(x+3{)}^2+(y-5{)}^2=25$
4. $(x-3{)}^2+(y-5{)}^2=25$

Q. If the intercepts of the variable circle on the $x$ and $y$-axis are $2$ units and $4$ units respectively, then the locus of the centre of the variable circle is

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

Q. The number of circles which passes through the origin and makes intercept of length $8$ units and $6$ units on the coordinate axes respectively, is

Q. A circle with radius $2$ units passing through origin, cuts the $x-$ axis and $y-$ axis at $A$ and $B$ respectively. The locus of centroid of the triangle $OAB$ is

1. $x^2+y^2=4$
2. $x^2+y^2=\frac{16}{9}$
3. $x^2+y^2=16$
4. $x^2+y^2=9$

Q.

If the line $x-2y=k$ cuts off a chord of length 2 from the circle $x^2+y^2=3$, then k =

1. 0

2. 

3. 

4. 

Q.

The equation of the circle which touches both axis and whose centre is $x_1,y_1$ is

1. 

2. 

3. 

4. 

Q.

Find the equation of a circle which touches both the axes and the line $3x-4y+8=0$ and lies in the third quadrant.

Q.

The circle $x^2+y^2-2x-2y+1=0$ is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in es new-position.

Q. Let $f\left(n\right)$ be the number of regions in which $n$ coplanar circles can divide the plane. If it is known that each pair of circles intersect in two different points and no three of them have common point of intersection, then

1. $f\left(15\right)=212$
2. $f^{-1}\left(134\right)=12$
3. $f\left(n\right)$ is always an even number
4. $f\left(n\right)$ is a perfect square

Q. The equation of a circle whose radius is $8$ units and which touches both $x-$axis and $y-$axis is

1. $x^2+y^2-16x-16y+64=0$
2. $x^2+y^2+16x-16y+64=0$
3. $x^2+y^2+16x+16y+64=0$
4. $x^2+y^2-16x+16y+64=0$

Q. Equation of circle passing through the origin and making intercepts of length $10$ units and $12$ units on $x$ axis and $y$ axis respectively, can be

1. $x^2+y^2+5x+6y=0$
2. $x^2+y^2-10x-12y=0$
3. $x^2+y^2+10x-12y=0$
4. $x^2+y^2-10x+12y=0$

Q. A circle of radius $7$ units touches the coordinate axes in the second quadrant. If the circle makes five complete rolls along the positive direction of $x-$axis, then the equation of circle in new position is
$(\text{Assume}\pi =\frac{22}{7})$

1. $(x-213{)}^2+(y-7{)}^2=49$
2. $(x-227{)}^2+(y+7{)}^2=49$
3. $(x+213{)}^2+(y+7{)}^2=49$
4. $(x+227{)}^2+(y-7{)}^2=49$

Q. If $(h,k)$ is the centre of the circle touches $y-\text{axis}$ at a distance of $12\text{units}$ from the origin and makes an intercept of $10\text{units}$ on $x-\text{axis}$, then the equation of circle for which $(h+k)$ is minimum, is

1. $(x-13{)}^2+(y+12{)}^2=169$
2. $(x+13{)}^2+(y-12{)}^2=169$
3. $(x-13{)}^2+(y-12{)}^2=169$
4. $(x+13{)}^2+(y+12{)}^2=169$

Q.

How do you write the standard form of a circle?

Q. If $A(a,0,0)$ and $B(0,b,0)$ are two vertices of a triangle whose third vertex lies on the curve $y^2=2x-3z$, then the locus of the centroid of the triangle is

1. $9y^2-6x-6by+9az+b^2+2a=0$
2. $9y^2-6x-6by+9z+b^2+2a=0$
3. $9y^2-6bx-6y+9z+b^2+2a=0$
4. $9y^2-6bx-6y+9az+b^2+2a=0$

Q. The length of intercepts made by the circle $x^2+y^2-4x+6y+4=0$ on $X$ and $Y$ axis respectively, are

1. $0,2\sqrt{5}$
2. $2\sqrt{5},0$
3. $0,2$
4. $0,0$

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. 3

2. 5

3. 6

4. 4

Q. The equation of a circle whose $x$-coordinate of the centre is $5$ and radius is $4$ units and also touches the $x$-axis, is

1. $x^2+y^2-10x+8y+49=0$
2. $x^2+y^2-10x-8y+25=0$
3. $x^2+y^2+8x-10y+25=0$
4. $x^2+y^2-16x-9y-25=0$

Q.

A circle touches positive $x-$axis at a distance of $9$ units from the origin and makes an intercept of $24$ units on negative direction of $y-$axis. Then

1. Radius of circle is $15$ units.
2. Equation of circle is $(x-9{)}^2+(y+15{)}^2={15}^2$.
3. Radius of circle is $13$ units.
4. Equation of circle is $(x-9{)}^2+(y+13{)}^2={13}^2$.

Q. Equation of circle passing through the origin and making intercepts of length $10$ units and $12$ units on $x$ axis and $y$ axis respectively, can be

1. $x^2+y^2+5x+6y=0$
2. $x^2+y^2-10x-12y=0$
3. $x^2+y^2+10x-12y=0$
4. $x^2+y^2-10x+12y=0$