Obtaining Centre and Radius of a Circle from General Equation of a Circle

Q.

Find the equation of chord of contact of the point (3, 5) on the circle $x^2+y^2+12x+8y+7=0$.

1. 9x - y - 5 = 0

2. 9x + y + 5 = 0

3. 13x - 2y +1 =0

4. 13 x + 2y - 1 = 0

Q. If two distinct chords drawn from the point (p, q) on the circle $x^2+y^2-px-qy=0(wherepq\ne 0)$ are bisected by the x-axis, then

1. $p^2=q^2$
2. $p^2=8q^2$
3. $p^2<8q^2$
4. $p^2>8q^2$

Q. If a chord of the circle $x^2$ + $y^2$ = 8 makes equal intercepts of length a on the coordinate axes then $\left|a\right|$ $<$

1. 2
2. 
3. 4
4. 

Q.

Find the centre of a circle passing through points $(6,-6),(3,-7)$ and $(3,3)$

Q. If OA, OB are two equal chords of the circle $x^2+y^2-2x+4y=0$ perpendicular to each other and passing
through the origin, then the equations of OA and OB are

1. 3x – y = 0, x + 3y = 0
2. 3x – y = 0, x – 3y = 0
3. 3x + y = 0, x – 3y = 0
4. 3x + y = 0, x + 3y = 0

Q. If $y=2\left[x\right]+3$ and $y=3\left[x\right]-1,$ find the value of $[x+y]$, Where $[.]$ denotes GIF.

Q. The center of the circle given by the equation $x^2+y^2-4x+6y-51=0$ is .

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

Q.

If two circles $(x-1{)}^2+(y-3{)}^2=r^{2}and{x}^2+y^2-4x-4y+4=0$ intersect in two distinct point then

1. 2 < r < 8

2. r < 2

3. r = 2

4. r > 2

Q.

The centre and radius of the circle $x^2+y^2+2gx+2yf+c=0$ are

1. $(g,f)$ and $\sqrt{g^2+f^2-c}$

2. $(-g,-f)$ and $\sqrt{g^2+f^2-c}$

3. $(g,f)$ and $\sqrt{g^2+f^2+c}$

4. $(-g,-f)$ and $\sqrt{g^2+f^2+c}$

Q. 7. x2 + y2-4x-8y-45 = 0

Q.

$(2+2\lambda +\mu )x^2+(1+2\lambda +2\mu )y^2+(3+5\lambda +3\mu )xy$

$-(16+14\lambda +11\mu )x-(10+13\lambda +17\mu )+(24+20\lambda +30\mu )=0$ is an equation of circle only when

1. $\lambda =1\mu =1$

2. $\lambda =-2\mu =\frac{-12}{11}$

3. $\lambda =1\mu =0$

4. $\lambda =\frac{-6}{5}\mu =1$

Q. Find the centre and radius of the circle $x^2+y^2-4x-8y-45=0$.

Q. Find the equation of the circle with centre $(\frac{1}{2},\frac{1}{4})$ and radius $\frac{1}{12}$

Q.

The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is

1. 

2. 

3. 

4. 

Q. 6, (х + 5)2 + (у-3)2-36

Q. If $\left\{x\right\}$ and $\left[x\right]$ represent the fractional and the integral part of $x$ respectively, then $\frac{2019}{2020}\left[x\right]+\frac{x}{2020}+\sum _{r=1}^{2019}\frac{\{x+r\}}{2020}$ is equal to

1. $1010x$
2. $x$
3. $\frac{1}{2021}x$
4. $2021x$

Q. 8. x2 + y2-8x + 10y-12=0

Q. The value of the expression $\left[\frac{10}{27}\right]+\left[\frac{11}{27}\right]+\left[\frac{12}{27}\right]+...+\left[\frac{35}{27}\right]$ is

Q. $\mathrm{The}\mathrm{domain}\mathrm{of}f\left(x\right)={\sin }^{-1}\left(2x^2-3\right],\mathrm{where}[.]\mathrm{denotes}\mathrm{the}\mathrm{greatest}\mathrm{integer}\mathrm{function},\mathrm{is}$

1. $(-\sqrt{\frac{5}{2}},-1]\cup [1,\sqrt{\frac{5}{2}})$
2. $(-\sqrt{\frac{3}{2}},-1]\cup \left(-\sqrt{\frac{5}{2}},\sqrt{\frac{5}{2}}\right)$
3. $\left(-\sqrt{\frac{3}{2}},\sqrt{\frac{3}{2}}\right)$
4. $\left(-\sqrt{\frac{5}{2}},\sqrt{\frac{5}{2}}\right)$

Q. If $0<x<1000$ and $\left[\frac{x}{2}\right]+\left[\frac{x}{3}\right]+\left[\frac{x}{5}\right]=\frac{31}{30}x$ where [.] GIF; the number of possible values of x is