Definition of Circle

Q. If $x^2+y^2=25,$ then the maximum value of ${\log }_5|3x+4y|$ is

Q. If a circle and a square have the same perimeter, then

1. Their areas are equal

2. Area of circle is larger

3. Area of square is larger

4. None of these

Q. $a{x}^2+2y^2+2bxy+2x-y+c=0$ represents a circle through the origin, if

1. a = 0, b = 0, c = 2

2. a = 2, b = 2, c = 0
3. a = 2, b = 0, c = 0
4. a = 1, b = 0, c = 0

Q.

If one end of the diameter is $(1,1)$ and other end lies on the line $x+y=3$, then locus of centre of circle is

1. $2(x-y)=5$
2. $2x+2y=5$
3. $x+y=1$
4. None of these

Q. The equation $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$ will represent a circle, if

1. a = b ≠ 0 and h = 0
2. f = g and h = 0
3. f = g and c = 0

4. a = b = 0 and c = 0

Q. The centre of circle inscribed in square formed by the lines $x^2$ - 8x + 12 = 0 and $y^2$ - 14y + 45 = 0, is

1. (9, 4)

2. (7, 4)

3. (4, 9)

4. (4, 7)

Q. A variable circle passes through the fixed point (2, 0) and touches the y-axis . Then the locus of its centre is

1. A circle

2. A hyperbola
3. A parabola

4. An Ellipse

Q. The centre of the circle $x=-1+2cos\theta ,y=3+2sin\theta ,$ is

1. (1, -3)
2. (-1, 3)
3. (1, 3)
4. None of these

Q. The equation of the circumcircle of the triangle formed by the lines $y+\sqrt{3}x=6,y-\sqrt{3}x=6,$ and $y=0,$ is

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

Q. The area of a circle whose centre is (h, k) and radius a is

1. $\pi (h^2+k^2-a^2)$
2. $\pi (a^{2}hk$
3. $\pi (a^2$
4. None of these