Definition of circle

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

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. An Ellipse

3. A parabola
4. A hyperbola

Q. The equation $2x^2+2y^2+4x+8y+15=0$ represents

1. A pair of straight lines

2. A circle

3. An ellipse
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 c = 0

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

Q. Question 5
Write whether the following statement is True or False?
The coordinate of points in the table.
$\begin{array}{cccccc}X& 0& 1& 2& 3& 4\\ Y& 2& 3& 4& -5& 6\end{array}$
Represent some of the solutions of the equation x - y + 2 = 0.

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. Four distinct points (2k, 3k), (1, 0) (0, 1) and (0, 0) lie on a circle for

1. ∀ k ∈ I
2. For two values of k
3. 0 < k < 1
4. k < 0

Q. Find the perpendicular distance of the point $(3,4)$ from the line $6x+8y=5$.

Q. A Straight line through p(-15, -10), meets the straight line x - y -1 = 0, x + 2y = 5 and x + 3y = 7 respectively at A, B and C. If $\frac{12}{PA}+\frac{40}{PB}=\frac{52}{PC},$ then prove that the straight line passes through origin.

Q. John made the given grid to show the location of some things in his garden. Which ordered pair best represents the point on the grid labelled "Tree" ?

1. $(2,6)$
2. $(1,3)$
3. $(3,1)$
4. Noneofthese

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

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

Q.

Two parallel chords of a circle of radius 2 units are at a distance $\sqrt{3}+1$ units apart. If the chords subtend at the centre, angles of $\frac{\pi }{k}$ and $\frac{2\pi }{k}$, where $k>0$, then the value of [k] (where [k] denotes the largest integer less than or equal to k) is ___

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. None of these

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

Q.

The values of $\lambda$ for which the circle $x^2+y^2+6x+5+\lambda (x^2+y^2-8x+7)=0$ dwindles into a point are

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

2. $1\pm \frac{\sqrt{2}}{3}$
   

3. $2\pm \frac{2\sqrt{2}}{3}$
   

4. $2\pm \frac{4\sqrt{2}}{3}$
   

Q. Two vertices of an equilateral triangle are (–1, 0) and (1, 0) and its third vertex lies above the x-axis, the equation of the circumcircle is

1. 
2. 
3. 
4.