# Director Circle

## Trending Questions

**Q.**The equation of director circle of the circle x2+y2=a2 is

- None of these
- x2+y2=4a2
- x2+y2=√2a2
- x2+y2−2a2=0

**Q.**The equation of the director circle of the circle (xâˆ’2)2+(y+3)2=16 is

- x2+y2âˆ’4x+6y=45
- x2+y2âˆ’4x+6y=19
- x2+y2âˆ’4x+6y=51
- x2+y2âˆ’4x+6y=77

**Q.**If two tangents drawn from a point P to the parabola y2=16(x–3) are at right angles, then the locus of point P is

- x+2=0
- x+4=0
- x+1=0
- x+3=0

**Q.**The number of points on the curve y=||1−ex|−2| from which mutually perpendicular tangents can be drawn to the parabola x2=−4y is

**Q.**Tangents are drawn to the circle x2+y2=50 from a point P lying on the x−axis. These tangents meet the y−axis at points P1 and P2. Possible coordinates of P so that area of △PP1P2 is minimum, are

- (10, 0)
- (10√2, 0)
- (−10, 0)
- (−10√2, 0)

**Q.**

Find the
real numbers *x* and *y* if (*x* â€“ *iy*) (3
+ 5*i*) is the conjugate of â€“6 â€“ 24*i*.

**Q.**

Tangent at any point on the hyperbola x2a2âˆ’y2b2=1 cut the axis at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by

None of these

**Q.**If the angle between the tangents drawn to the circle x2+y2+2gx+2fy+c=0 (c>0) from the origin is π2, then

- g2+f2=3c
- g2+f2=2c
- g2+f2=c
- g2+f2=4c

**Q.**The points of contact Q and R tangent from the point P(2, 3) on the parabola y2=4x are

- (1, 2), (4, 4)
- (9, 6), (14, 1)
- (9, 6), (1, 2)
- (4, 4), (9, 6)

**Q.**If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle x2+y2−2x+4y−11=0, is 6 units, then minimum distance of T from the director circle of the given circle is

- 6
- 12
- 6√2
- 12−4√2

**Q.**The equation of the circle C1 is x2+y2=4. The locus of the intersection of orthogonal tangents to the circle is the curve C2 and the locus of the intersection of perpendicular tangents to the curve C2 is the curve C3. Then

- C3 is a circle
- the area enclosed by the curve C3 is 8π
- C2 and C3 are circles with same centre
- radius of C3 is twice the radius of C2

**Q.**Let f(x, y)=0 be the equation of a circle such that f(0, y)=0 has equal real roots and f(x, 0)=0 has two distinct real roots. Let g(x, y)=0 be the locus of points ′P′ from where tangents to circle f(x, y)=0 make angle π3 between them and g(x, y)=x2+y2–5x–4y+c, c∈R. Let Q be a point from where tangents drawn to circle g(x, y)=0 are mutually perpendicular. If A, B are the points of contact of tangents drawn from Q to circle g(x, y)=0, then area of triangle QAB is

- 2512
- 252
- 258
- 254

**Q.**The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2 on the other circle for the given circle's equations x2+y2−10x−10y+41=0, x2+y2−24x−10y+160=0

**Q.**

The difference of the radii of the two circles with centre (4, 3) and touching the circle x2+y2=1, is

0

2

4

Not fixed

**Q.**

The equation of the circle passing through the points (4, 1), (6, 5) whose centre lies on the line 4x+y-16=0 is

x

^{ 2}+y^{2}-6x-8y+15=0x

^{ 2}+y^{2}-10x-6y+29=0x

^{ 2}+y^{2}-x-13=0x

^{ 2}+y^{2}+4y-12=0

**Q.**Let P(x, y) be a variable point such that |√(x−2)2+(y−3)2−√(x−6)2+(y−6)2|=4, then

- The locus of P is a hyperbola with eccentricity 54
- The locus of P is a hyperbola with eccentricity 53
- The locus of the intersection of perpendicular tangents to the locus of P is (x−4)2+(y−92)2=54
- The locus of the intersection of perpendicular tangents to the locus of P is (x−4)2+(y−92)2=74

**Q.**

If the ratio of the lengths of tangents from a point to the circles x2+y2+4x+3 = 0, x2+y2−6x+5 = 0 is 1:2 then the locus of P is a circle whose centre is

(-11/3 , 0 )

(-22/3 , 0 )

(-11 , 6 )

(-11/5 , 0 )

**Q.**A circle is concentric with the circle x2+y2−6x+12y+15=0 and has area double of its area. The equation of the circle is

- None of these

**Q.**Let f(x, y)=0 be the equation of a circle such that f(0, y)=0 has equal real roots and f(x, 0)=0 has two distinct real roots. Let g(x, y)=0 be the locus of points ′P′ from where tangents to circle f(x, y)=0 make angle π3 between them and g(x, y)=x2+y2–5x–4y+c, c∈R. Let Q be a point from where tangents drawn to circle g(x, y)=0 are mutually perpendicular. If A, B are the points of contact of tangents drawn from Q to circle g(x, y)=0, then area of triangle QAB is

- 2512
- 258
- 254
- 252

**Q.**TP and TQ are tangents to the parabola y2=4ax at points P and Q. If the chord PQ passes through a fixed point (–a, b), then the locus of T is

- by=2a(x–a)
- ax=2b(y–b)
- bx=2a(y–a)
- ay=2b(x–b)

**Q.**

Find the equation of director circle of a circle whose equation is x2+y2−4x+6y+12=0

x2+y2−4x+6y+11=0

x2+y2−4x+6y+12=0

x2+y2−2x+3y+11=0

x2+y2−4x+6y+1=0

**Q.**

Find the equation of director circle of the circle (x−1)2+(y−2)2=4

(x−1)2+(y−2)2=4√2

(x−1)2+(y−2)2=8

(x+1)2+(y+2)2=4√2

(x−2)2+(y−1)2=8

**Q.**

AB is a chord of the parabola y2=4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

a

2a

4a

8a

**Q.**Find the center and radius of the circle whose equation is given by x2+y2+4y=0

**Q.**Find the equations of the tangent and normal to the parabola y2=8x at (2, 4).

**Q.**Let PQ be a focal chord of the parabola y2=4ax. The tangents to the parabola at P and Q meet at a point lying on the line y=2x+a, a>0.

Length of chord PQ is

- 2a
- 7a
- 5a
- 3a

**Q.**Match List I with the List II and select the correct answer using the code given below the lists :

List IList II(A)Radius of the largest circle which passes through the focus of the parabola y2=4x and is completely(P)16 contained in it, is(B)If the shortest distance between the curves y2=4x and y2=2x–6 is d , then d2 is (Q)5(C)Let AB be a focal chord of y2=12x with focus S. The harmonic mean of lengths of segments AS(R)6 and BS is (D)Tangents drawn from P meet the parabola y2=16x at A and B. If these two tangents are (S)4 perpendicular, then the least value of √AB is

Which of the following is CORRECT ?

- (C)→(R), (D)→(S)
- (C)→(P), (S)→(Q)
- (C)→(Q), (D)→(Q)
- (C)→(R), (D)→(Q)

**Q.**Assertion :The maximum value of (√−3+4x−x2+4)2+(x−5)2 (where 1≤x≤3) is 36. Reason: The maximum distance between the point (5, −4) and the point on the circle (x−2)2+y2=1 is 6.

- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Both Assertion and Reason are incorrect

**Q.**

Which of the following statements is/are correct?

1. The locus of the point of intersection of two perpendicular tangents is called director circle of the given circle.

2. The director circle of a circle is concentric circle.

3. The radius of director circle of a circle is equal to the radius of original circle.C

Only 1 & 2

Only 1

Only 1 & 3

All 1, 2 and 3

**Q.**If the tangent at the point P(2, 4) to the parabola y2=8x meets the parabola y2=8x+5 at Q and R, then the midpoint of QR is

- (2, 4)
- (4, 2)
- (7, 9)
- none of these