Equation of Circle with Origin as Center

Q.

A circle which touches the positive axes, and whose centre it at distance $2\sqrt{2}$ from the origin, then the equation is

1. x²+y²+4x+4y=0

2. x ²+y²+4x+4y+2=0

3. 

4. x ²+y² - 4x-4y+4=0

Q.

For line segment AB slope of the line is $\frac{BC}{AC}$

1. True

2. False

Q. If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ at four points
$P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3),andS(x_4,y_4)$, then

1. $x_1+x_2+x_3+x_4=0$
2. $y_1+y_2+y_3+y_4=0$
3. $x_1{x}_2{x}_3{x}_4=c^4$
4. $y_1{y}_2{y}_3{y}_4=c^4$

Q. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of $\frac{2\pi }{3}$ at its centre is

1. 
2. 
3. 
4. 

Q.

An isosceles right angled triangle is inscribed in the circle $x^2+y^2=r^2.$ If the coordinates of an end of the hypotenuse are (a, b), the coordinates of the vertex are

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

Q. The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is

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

Q. The centres of the circles $x^2+y^2=1,$ $x^2+y^2+6x-2y=1$ and $x^2+y^2-12x+4y=1$ are

1. same
2. Collinear
3. Non–collinear
4. None of these

Q. The equation of the image of the circle $x^2+y^2$ - 6x - 4y + 12 = 0 by the line mirror x + y - 1 = 0

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

Q. The number of points with integral coordinates that are interior to the circle $x^2+y^2=16$ is

1. 43
2. 49
3. 45
4. 51

Q. The intercept on the line y = x by the circle $x^2+y^2-2x=0$ is AB. The equation of the circle on AB as a diameter is

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