# Equation of Circle in Complex Form

## Trending Questions

**Q.**The area of the region {(x, y):0≤x≤94, 0≤y≤1, x≥3y, x+y≥2} is

- 1132 sq. units.
- 3596sq. units.
- 3796 sq. units.
- 1332sq. units.

**Q.**Let P and Q be two distinct points on a circle which has centre at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to

- {(2+2√2, 3+√5), (2−2√2, 3−√5)}
- {(4, 0), (0, 6)}
- {(−1, 5), (5, 1)}
- {(2+2√2, 3−√5), (2−2√2, 3+√5)}

**Q.**Let z1 and z2 be two complex numbers satisfying |z1|=9 and |z2−3−4i|=4. Then the minimum value of |z1−z2| is :

- 0
- 1
- √2
- 2

**Q.**The least value of |z−3−4i|2+|z+2−7i|2+|z−5+2i|2 occurs when z=x+iy then the value of x is

**Q.**

The area of the circle centred at$(1,2)$and passing through $(4,6)$ is

$5\mathrm{\xcf\u20ac}\mathrm{sq}\mathrm{units}$

$10\mathrm{\xcf\u20ac}\mathrm{sq}\mathrm{units}$

$25\mathrm{\xcf\u20ac}\mathrm{sq}\mathrm{units}$

None of these

**Q.**Each of the circles |z−1−i|=1 and |z−1+i|=1 where z=x+iy, touches internally a circle of radius 2 units. The equation of the circle touching all the three circles can be

- 3z¯¯¯z+z+¯¯¯z−1=0
- 3z¯¯¯z−7z−7¯¯¯z+15=0
- z¯¯¯z−z−¯¯¯z−3=0
- 3z¯¯¯z+z+¯¯¯z+1=0

**Q.**If |z−1−i|=1, then the locus of a point represented by the complex number 5(z−i)−6 is

- a circle with centre (−1, 0) and radius 5
- a line passing through the origin
- a line passing through (−1, 0)
- a circle with centre (1, 0) and radius 3

**Q.**

The equation zÂ¯z+aÂ¯z+Â¯az+b = 0, bâˆˆR represents a circle if

None of these

**Q.**The region of argand diagram defined by \( |z-1|+|z+1|\leq 4\) is

- interior of an ellipse
- exterior of a circle
- interior and boundary of an ellipse
- None of the above

**Q.**Locus of a complex number satisfying arg((z−5+4i)(z+3−2i))=−π4 is arc of a circle

- whose radius is 5√2
- whose radius is 5
- whose length of arc os 15π√2
- whose centre is −2−5i

**Q.**The largest value of r for which the region represented by the set {ω∈C:|ω−4−i|≤r} is contained in the region represented by the set {z∈C:|z−1|≤|z+i|}, is equal to:

- 2√2 unit
- 32√2 unit
- √17 unit
- 52√2 unit

**Q.**The complex number having least positive argument and satisfying the inequality |z−5i|≤3 is

- 125+165i
- 125+125i
- 165+125i
- 35+45i

**Q.**

The area of the circle whose centre is at $(1,2)$ and which passes through the point $(4,6)$is:

$5\mathrm{\xcf\u20ac}$

$10\mathrm{\xcf\u20ac}$

$25\mathrm{\xcf\u20ac}$

None of these

**Q.**If z=x+iy and x2+y2=16, then the range of ∣∣|x|−|y|∣∣ is

- [0, 4]
- [0, 2]
- None of these
- [2, 4]

**Q.**

In a triangle, $ABC,AD,BE$, and $CF$ are the altitudes, and $R$ is the circumradius then the radius of the circle $DEF$ is

$2R$

$R$

$\frac{R}{2}$

None of these

**Q.**Equation of tangent drawn to circle |z|=r at the point A(z0) is

- Re(zz0)=1
- z¯¯¯z0−z0¯¯¯z=2r2
- Im(zz0)=1
- z¯¯¯z0+z0¯¯¯z=2r2

**Q.**If Re(1z)>12 and Re(z)>0, then which of the following is/are true about the locus of z?

- The locus of z is the region inside a circle.
- The locus of z is the region inside an ellipse.
- Area of locus is π sq. units
- Centre of the locus is (1, 0)

**Q.**Locus of complex number satisfying arg[(z−5+4i)(z+3−2i)]=−π4 is the arc of a circle

- whose radius is 5√2 units
- whose radius is 5 units
- whose length (of arc) is 15π√2 units
- whose centre is −2−5i

**Q.**Given that the two curves arg(z)=π6 and |z−2√3i|=r intersect in two distinct points, then

([r] represents integaral part of r)

- [r]=3
- 2<r<3
- [r]=2
- 3<r<2√3

**Q.**If Im(2z+1iz+1)=−3, then locus of z is

- a circle
- a parabola
- a straight line
- none of these

**Q.**Let C1 and C2 are concentric circles of radius 1 unit and 8/3 unit , respectively, having centre at (3, 0) on the Argand plane. If the complex number z satisfies the inequality

log1/3(|z−3|2+211|z−3|−2)>1 then

- z lies outside C1 but inside C2
- z lies inside C1
- z lies outside C2
- none of these

**Q.**For positive constant r, let M be the set of complex numbers z which satisfy |z−4−3i|=r. Then which of the following statements is (are) CORRECT?

- If r=3, then the minimum value of |z| for complex number z which belongs to M is 2.
- If r=3, then the maximum value of |z| for complex number z which belongs to M is 8.
- If r=5, then the complex number having least modulus which belongs to M is z=0
- If r=5, then the complex number having greatest modulus which belongs to M is z=8+6i

**Q.**If z is a complex number lying in the fourth quadrant of Argand plane and ∣∣∣[kzk+1]+2i∣∣∣>√2 for all real values of k (k≠−1), then range of arg(z) is

- None of these
- (−π4, 0)
- (−π8, 0)
- (−π6, 0)

**Q.**If |z|=1 and w=−1+3z, then the locus of w on argand plane is

- a circle whose centre is at (−1, 0) and radius is 3 units.
- a circle whose centre is at (−1, 0) and radius is 9 units.
- a circle whose centre is at (0, −1) and radius is 3 units.
- a circle whose centre is at (1, 0) and radius is 3 units.

**Q.**If t and c are two complex numbers such that |t|≠|c|, |t|=1 and z=at+bt−c, z=x+iy, then locus of z is (where a, b are complex numbers)

- line segment
- straight line
- ellipse
- circle

**Q.**For equation |z−z1|2+|z−z2|2=a to represent a circle, which of the following is/are true?

- Centre of the circle is (z1+z2)4.
- Centre of the circle is (z1+z2)2.
- The circle is real, if 2a≥|z1−z2|2.
- The circle is real, if 4a≥|z1−z2|2.

**Q.**Let A(z1) be the point of intersection of curves arg(z−2+i)=3π4 and arg(z+√3i)=π3. B(z2) is the point on arg(z+√3i)=π3 such that |z2−5| is minimum, and C(z3) is the centre of circle |z−5|=3. If the area of triangle ABC is √k sq. units, then the value of k is

**Q.**For equation |z−z1|2+|z−z2|2=a to represents a circle, which of the following is/are true

- Centre of the circle is (z1+z2)4.
- Centre of the circle is (z1+z2)2.
- The circle is real, if 2a≥|z1−z2|2.
- The circle is real, if 4a≥|z1−z2|2.

**Q.**

Find the area of the region bounded by line x = 2 and parabola y2=8x.

**Q.**If the complex number z=x+iy satisfies the condition |z+1|=1 , then z lies on

- Circle with centre (−1, 0) and radius 1
- y−axis
none of these

- x−axis