# Definition of Circle

## Trending Questions

**Q.**The equation x2+y2+4x+6y+13=0 represents

- a circle with radius 5 units
- a pair of two distinct straight lines
- a pair of coincident straight lines
- a point circle

**Q.**

The diameter of the circle 9x2+y2 = 4(X2−Y2)−8X is

4/5

8/5

8

Does not exit

**Q.**The equation(s) of the circle(s) having radius 5, centre on the line y=x and touching both the coordinate axes is(are)

- x2+y2+10x+10y+25=0
- x2+y2−10x+10y+25=0
- x2+y2+10x−10y+25=0
- x2+y2−10x−10y+25=0

**Q.**A variable straight line through A(−1, −1) is drawn to cut the circle x2+y2=1 at the points B, C. If P is chosen on the line ABC such that AB, AP, AC are in H.P then the locus of P is

- x+y+1=0
- x+y−1=0
- x−y+1=0
- x−y−1=0

**Q.**

Area of the shaded regions in given figure is 25(6−π)cm2and diameter of semicircle drawn inside the given rectangle is 10 cm. Then the shortest distance between the two semicircles in (in cm)

5

10

15

20

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

- π(h2+k2−a2)
- π(a2hk
- π(a2
- None of these

**Q.**

If a chord of the circle x2+y2−4x−2y−c=0 is trisected at the points (1/3, 1/3) and (8/3, 8/3), then

- Length of the chord=7√2
- c=20
- Radius of the circle 25
- c=25

**Q.**If the two lines x+y=6 and x+2y=4 are the diameters of the circle which passes through (2, 6), then its equation is

- x2+y2−16x+4y+32=0
- x2+y2−16x+4y+23=0
- x2+y2−16x+4y−32=0
- x2+y2−16x+4y−23=0

**Q.**The equation of the circle concentric with the circle x2+y2−8x+6y−5=0 and passing through the point (−2, −7) is

- x2+y2−8x+6y−30=0
- x2+y2−8x+6y−26=0
- x2+y2−8x+6y−27=0
- x2+y2−8x+6y=0

**Q.**If the endpoints of the diameter is P(3, 1) and Q(h, k) of the circle 2x2+2y2−2x−7y−7=0, then which of the following is/are correct?

- Q=(−1, 2)
- Q=(−2, 52)
- radius of circle is √674 units
- radius of circle is √1094 units

**Q.**

Translate each of the following statements into an equation.

The diameter ($d$) of a circle is twice its radius ($r$)

**Q.**The equation of the circle with centre (–3, 2) and radius 4 units is

- x2+y2+6x−4y−13=0
- x2+y2+6x−4y−3=0
- x2+y2+6x−4y−7=0
- x2+y2+6x−4y+3=0

**Q.**Let f(x, y)=0 be the equation of a circle. If f(0, λ)=0 has equal roots λ=2 and f(λ, 0)=0 has root λ=45, 5, then the centre of the circle is

- (2, 2910)
- (2910, 2)
- (−2, 2910)
- (2910, −2)

**Q.**If r is the radius of circle which touches both the coordinate axes and passes through (−2, 1), then which of the following is/are true?

- least value of r is 1.
- greatest value of r is 6.
- sum of all possible values of r is 6.
- there exist two circle with the given conditions.

**Q.**3. The equation of the circle passing through( 1, 0 )and (0, 1) having smallest possible radius ?

**Q.**If S is the equation of circle whose two diameters are 2x−y=3, x−2y=6 and area is 616 cm2, then which of the following is/are true?

(Take π=227)

- Radius of the circle is 14 cm
- Equation of the circle is x2+y2+6y−187=0
- Centre of the circle is (0, −3)
- Equation of the circle is x2+y2−6y−187=0

**Q.**Find the equation of parabola whose focus is (7, 0) and equation of directrix X=7

**Q.**The equation of a circle whose radius is 7 units and x−coordinate of the centre is −2 and also touches the x−axis, is

- x2+y2+4x−14y+4=0
- x2+y2+4x+14y+4=0
- x2+y2+4x−14y−49=0
- x2+y2+4x+14y+49=0

**Q.**The centre of circle x2+y2+16x−22y−20=0, is

- (8, 11)
- (−8, 11)
- (−16, 22)
- (11, −8)

**Q.**The equation of the circle circumscribing the triangle formed by the line x+y=6, 2x+y=4 and x+2y=5, is

- x2+y2−17x−19y+50=0
- x2+y2+17x+19x+50=0
- x2+y2−19x−17x+50=0
- x2+y2−19x−17x−50=0

**Q.**The equation of the circle which passes through (1, 2) and (0, 2) and has its radius as small as possible is

- x2+y2−2x−3y−2=0
- x2+y2−x−4y+4=0
- x2+y2−3x+4=0
- x2+y2+x+2y+1=0

**Q.**The equation of the circle inscribed in the triangle formed by the straight line 4x+3y=6 and both the coordinate axes is

- 5x2+5y2−5x−5y+11=0
- x2+y2−6x−6y+18=0
- 4x2+4y2−4x−4y+1=0
- 2x2+2y2−4x−4y+1=0

**Q.**The centre of circle inscribed in square formed by the lines x2 - 8x + 12 = 0 and y2 - 14y + 45 = 0, is

(9, 4)

- (4, 9)
(4, 7)

(7, 4)

**Q.**If an equilateral triangle of side a is inscribed in the circle x2+y2−6x−4y+5=0, then the value of a2 is

**Q.**Let z be an imaginary complex number satisfying |z−1|=1. If α=2z, β=2α and γ=2β, then the value of |z|2+|α|2+|β|2+|γ|2+|z−2|2+|α−4|2+|β−8|2+|γ−16|2 is

- 100
- 320
- 340
- 400

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

Their areas are equal

Area of circle is larger

Area of square is larger

- None of these

**Q.**If the abscissas and ordinates of two points P and Q are the roots of the equations x2−7x+10=0 and x2+7x+12=0 respectively, then the equation of the circle with PQ as diameter is

- x2+y2+5x+2y+10=0
- x2+y2−4x−3y+12=0
- x2+y2−7x+7y+22=0
- x2+y2−5x+2y+10=0

**Q.**The equation of the circle whose centre is on the line 2x−y−2=0 and passes through the points (3, −2) and (−2, 0) is

- x2+y2−x+2y=6
- x2+y2−x−2y=13
- x2+y2−6x+2y=9
- x2+y2−3x+2y=0

**Q.**A point moves in such a manner that the sum of the squares of its distances from the vertices of a triangle is constant. Then, the locus of the point is

- a hyperbola
- a parabola
- an ellipse
- a circle