Definition of Circle

Q. Question 5
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.

Q. Question 5
If AOBC is a rectangle whose three vertices are A(0, 3), 0(0, 0) and B(5, 0), then the length of its diagonal is:
(A) 5
(B) 3
(C) $\sqrt{34}$
(D) 4

Q. Find the equation of the circle passing through the points $(3,4),(3,2)$ and $(1,4)$

Q. From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown. Find the area of the remaining portion of the square.

Q. Question 5
If the perimeter of a circle is equal to that of square, then the ratio of their areas is:
(A) 22:7
(B) 14:11
(C) 7:22
(D) 11:14

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

1. A circle

2. A pair of straight lines

3. An ellipse
4. None of these

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

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

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

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

Q. Find the value of $k,$ if slope of line passing through $P(k,3)$ and $Q(1,2)$ is $-\frac{1}{3}$.

Q.

A square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. The coordinates of its vertices are

1. (-6, -9), (-6, 5), (8, 9) and (8, 5)

2. (-6, -9), (-6, 5), (8, -9) and (8, -5)

3. (-6, -9), (-6, 5), (8, -9) and (8, 5)

4. (-6, 9), (-6, -5), (8, -9) and (8, 5)

Q. If Four distinct points $(2,3),(0,2),(4,5)$ and $(0,t)$ are concyclic, then $t^3+17$ is equal to

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

Q. The co-ordinates of the point of trisection of the line segment joining the points $(-4,3)$ and $(2,-1)$ are

1. $(-2,\frac{5}{3})$
2. $(3,1)$
3. $(2,1)$
4. None of these

Q.

1. $\left(\frac{1}{2},3\right)$
2. $\left(-3,-\frac{1}{2}\right)$
3. $\left(0,-\frac{1}{2}\right)$
4. $\left(3,\infty \right)$

Q. The length of the base of a triangle is 4 cm smaller than the length of the altitude, and the area of the triangle is 96 $c{m}^2$. Find. the lengths of the base and the altitude of the triangle.

Q. If $A(x,3)$ lies on perpendicular bisector of the line segment joining the point $P(4,8)$ and $Q(-4,0)$ find $x$.

Q. Question 3
If the circumference of a circle and the perimeter of a square are equal, then:
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square.

Q. Find the equation of the circle which is concentric with the circle $2x^2+2y^2+3x-4y+5=0$ and whose radius is $2\sqrt{5}$ units.

1. $4x^2+4y^2+6x-8y-55=0$
2. $4x^2+4y^2+6x-8y+90=0$
3. $4x^2+4y^2+6x-8y+57=0$
4. $4x^2+4y^2+6x-8y+87=0$

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

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

Q. If $1$ lies between the roots of the equation $y^2-my+1=0$ and $\left[x\right]$ is the GIF function,
then the value of $\left[{\left(\frac{4|x|}{|x{|}^2+16}\right)}^m\right]$, is

1. $0$
2. $1$
3. None of the above.
4. $2$

Q. If the vertices P, Q, R of a triangle PQR are rational points, which of the following points of the triangle PQR is/(are) always rational points(s).

1. Centroid
2. Incentre
3. Circumcentre
4. Othocentre

Q. The image of the point $(-1,3)$ across the line $x-y=0$ is

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