Equation of Circle Whose Extremities of a Diameter Given

Q.

The equation of the circle which touches both the axes and whose radius is a, is

1. 

2. 

3. 

4. 

Q.

Find the equation of the circle, the end points of whose diameter are (2, -3) and (-2, 4).
Find its centre and radius.

Q.

The abscissae of the two points A and B are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are the roots of the equation $x^2+2px-q^2=0$. Find the equation of the circle with AB as diameter. Also, find its radius.

Q. A variable circle passes through the fixed point A(p, q) and touches the x-axis. The locus of the other end of the diameter through A is

1. $(y-q{)}^2=4px$
2. $(x-q{)}^2=4py$
3. $(y-p{)}^2=4qx$
4. $(x-p{)}^2=4qy$

Q.

Find the equation of the circle the end points of whose diameter are the centre of the circles
$x^2+y^2-6x-14y-1=0$
and $x^2+y^2-4x+lOy-2=0$

Q.

Find the equation of the circle which circumscribes the triangle formed by the lines $x=0,y=0$ and $lx+my=1$.

Q. The equation of the circle drawn with the two foci of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ as the end-points of a diameter is

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

Q.

Equation of the circle with centre (1, 2) and passing through (2, 1) is

1. x ²+y²-6x+10y+18=0

2. x ²+y²+6x-10y+18=0

3. x ²+y²-6x+10y+25=0

4. x ²+y²-2x-4y+3=0

Q. The equation of the circle in diameter form with centre $(4,–2)$ and passing through the point $(2,-2)$ is

1. $(x-2)(x+6)+(y+3)(y-2)=0$
2. $(x+4)(x+2)+(y-1)(y+2)=0$
3. $(x-6)(x+2)+(y-4)(y+2)=0$
4. $(x-6)(x-2)+(y+2)(y+2)=0$

Q.

Find the equation of a line parallel to X-axis and passing through the origin.

Q.

ABCD is a square whose side is a ; taking AB and AD as axes, prove that die equation of the circle circumscribing the square is $x^2+y^2-a(x+y)=0$.

Q. If the vertices of a triangle be (2, –2), (–1, –1) and (5, 2), then the equation of its circum circle is

1. 
2. 
3. 
4. None of these

Q.

Find the equation of the circle circumscribing the rectangle whose sides are
$x-3y=4,3x+y=22,x-3y=14$ and $3x+y=62$.

Q. If $y+3x=0$ is the equation of a chord of the circle, $x^2+y^2–30x=0$, then the equation of the circle with this chord as diameter is

1. $x^2+y^2-3x-9y=0$
2. $x^2+y^2+3x+9y=0$
3. $x^2+y^2-3x+9y=0$
4. $x^2+y^2+3x-9y=0$

Q.

$Theequationofcircum-circleofa\Delta ABCis{x}^2+y^2+3x+y-6=0.IfA=(1,-2),B(-3,2)andthevertexCvariesthenthelocusofortho-centreof\Delta ABCisa$

1. Circle

2. Parabola

3. Ellipse

4. Straight line

Q. Let $d_1$ and $d_2$ be the lengths of the perpendiculars drawn from any point of the line $7x-9y+10=0$ upon the lines $3x+4y=5$ and $12x+5y=7$ respectively. Then

1. $d_1>d_2$
2. $d_1=d_2$
3. $d_1<d_2$
4. $d_1=2d_2$

Q.

The equation of the circle passing through the point (2, -1) and having two diameters along the pair of lines $2x^2+6y^2-x+y-7xy-1=0is$

1. 

2. 

3. 

4. 

Q.

If the equations of two diameters of a circle arc 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.

Q.

The sides of a square are x= 6, x =9, y = 3 and y = 6.
Find the equation of a circle drawn on di diagonal of the square as its diameter.

Q. If the line $y=4x-2$ cuts the curve $y^2=8x$ at points $A$ and $B,$ then the equation of circle having $AB$ as a diameter, is

1. ${(x+\frac{1}{2})}^2+y^2-\frac{x}{2}-2y-4=0$
2. ${(x-\frac{1}{2})}^2+y^2-\frac{x}{2}-2y-4=0$
3. ${(x-\frac{1}{2})}^2+y^2-\frac{x}{2}+2y-4=0$
4. ${(x-\frac{1}{2})}^2+y^2+\frac{x}{2}-2y-4=0$

Q.

The line $2x-y+6=0$ meets the circle $x^2+y^2-2y-9=0$ at A and B. Find the equation of the circle on AB as diameter.

Q. The equation of straight line passing through (-a, 0) and making the triangle with axes of area ‘T’ is

1. 
2. 
3. 
4. 

Q. If one end of a diameter of the circle $x^2+y^2-4x-6y+11=0$ be (3, 4), then the other end is

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

Q.

If the abscissae and ordinates of two points P and Q are roots of the equations $x^2+2ax-b^2=0$
and $x^2+2px-q^2=0$ respectively,
then write the equation of the circle with PQ as diameter.

Q. B & C are fixed points having co-ordinates (3, 0) and (–3, 0) respectively. If the vertical angle BAC is ${90}^{\circ }$, then the locus of the centroid of the $\Delta ABC$ has the equation.

1. $x^2+y^2=9$
2. $x^2+y^2=2$
3. $9(x^2+y^2)=1$
4. $9(x^2+y^2)=4$

Q. If the equation of a circle is $\lambda x^2+(2\lambda -3)y^2-4x+6y-1=0$ then the coordinates of centre are

1. $(\frac{2}{3},1)$
2. $(\frac{4}{3},-1)$
3. $(\frac{2}{3},-1)$
4. $(-\frac{2}{3},-1)$

Q. If the line $2y=4x-6$ cuts the curve $y^2=-16x$ at points $A$ and $B$, then the equation of circle having $AB$ as diameter is

1. $x^2+y^2-x+8y+\frac{105}{4}=0$
2. $x^2+y^2-x-8y+\frac{105}{4}=0$
3. $x^2+y^2+x+8y+\frac{105}{4}=0$
4. $x^2+y^2+x+8-\frac{105}{4}=0$

Q. Find the direction cosines of the line which is perpendicular to the lines whose direction ratios are 1, -1, 2 and 2, 1, -1.

Q.

Find the equation of the circle which touches the x-axis at a distance of 3 from the origin and cuts an intercepts of 6 on the y-axis.

1. $x^2+y^2-6x-6\sqrt{2}y+9=0$

2. $x^2+y^2+6x-6\sqrt{2}y+9=0$

3. $x^2+y^2-6x-6\sqrt{2}y+9=0$

4. $x^2+y^2+6x+6\sqrt{2}y+9=0$

Q. The radius of the circle $(x-5)(x-1)+(y-8)(y-4)=0$ is

1. $4$ units
2. $2\sqrt{2}$ units
3. $3\sqrt{2}$ units
4. $8$ units