# Equation of a Chord with a Given Middle Point

## Trending Questions

**Q.**

The locus of the midpoints of a chord of a circle ${x}^{2}+{y}^{2}=4$, which subtends a right angle at the origin, is

${x}^{2}+{y}^{2}=1$

${x}^{2}+{y}^{2}=2$

$x+y=1$

$x+y=2$

**Q.**

The equation of the circle which intersects circles x2+y2+x+2y+3=0, x2+y2+2x+4y+5=0 and

x2+y2âˆ’7xâˆ’8yâˆ’9=0 at right angle, will be

**Q.**Locus of mid point of chords of x2+y2+2gx+2fy+c=0 that pass through the origin, is

- x2+y2+2gx+2fy+c=0
- x2+y2+gx+fy+c=0
- x2+y2+gx+fy=0
- 2(x2+y2+gx+fy)+c=0

**Q.**

Equation of the diameter of the circle x2+y2−2x+4y=0 which passes through the origin is

x+2y=0

x−2y=0

2x+y=0

2x−y=0

**Q.**If tangents are drawn from points on the hyperbola x24−y29=1 to the circle x2+y2=4, then the locus of the mid-point of the chord of contact is

- x2+y2=x29−y24
- (x2+y2)2=x24−y29
- (x2+y2)2=16(x24−y29)
- (x2+y2)2=9(x29−y24)

**Q.**The equation of diameter which bisects the chord 3x+y+5=0 of the circle x2+y2=16 is

- 3x+y=0
- x+3y=0
- 3x−y=0
- x−3y=0

**Q.**The equation of the chord of the circle x2+y2=r2 passing through (2, 3) and farthest from the centre is

- x−3y+7=0
- 2x+y−7=0
- 2x+3y−13=0
- x+y−5=0

**Q.**The locus of midpoint of the chord of contact of x2+y2=2 from the points on 3x+4y=10 is a circle whose centre is

- (45, 35)
- (35, 45)
- (410, 310)
- (310, 410)

**Q.**Let circle be 2x(x−a)+y(2y−b)=0, a≠0, b≠0. Then the condition on a and b if two chords each bisected by the x-axis, can be drawn to the circle from (a, b2), is

- None of these
- a2>2b2
- a2<2b2
- a2=2b2

**Q.**Let x−2y+7=0 be a chord of the circle x2+y2−2x−10y+1=0. If the midpoint of the chord is P(α, β), then the value of 5|α−β| is

**Q.**The equation of the diameter of the circle x2+y2+2x−4y−4=0 which is parallel to 3x+5y−4=0 is

- 3x+5y=−7
- 3x+5y=7
- 3x+5y=9
- 3x+5y=1

**Q.**If tangents PA and PB are drawn to x2+y2=9 from any arbitrary point P on the line x+y=25, then the locus of mid point of chord AB is

- 25(x2+y2)=3(x+y)
- 25(x2+y2)=9(x+y)
- 5(x2+y2)=3(x+y)
- 5(x2+y2)=9(x+y)

**Q.**If the circle C1:x2+y2=16 intersects another circle C2 of radius 5 in such a manner that common chord is of maximum length and has a slope equal to 34, then the absolute sum of coordinates of the centre C2 is

**Q.**Let 3x−y−3=0 is a diameter of the circle x2+y2−4x−6y+4=0. If L1 is the chord which is bisected by the given diameter line, then which of the following is/are true?

- When L1 is the largest possible chord of the circle, its possible equation is x+3y−11=0
- When L1 is the largest possible chord of the circle, its possible equation is x−3y+8=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11+√10=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11−√10=0

**Q.**OPQR is a square and M, N are the middle points of the sides PQ and QR, respectively, then the ratio of the areas of the square and the △OMN is

- 4:1
- 8:3
- 2:1
- 7:3

**Q.**A line y=mx+1 intersects the circle (x−3)2+(y+2)2=25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate −35, then which one of the following options is correct?

- 2≤m<4
- 4≤m<6
- 6≤m<8
- −3≤m<−1

**Q.**

What is the equation of the chord centered at (1, 2) in the circle x2 + y2 − 4x − 6y − 10 = 0

x − y − 3 = 0

x − y + 3 = 0

x +y − 3 = 0

x + y + 3 = 0

**Q.**Chords of contact are drawn from the points on a tangent of a hyperbola x2−y2=16 to a parabola y2=16x. If all the chords of contact pass through a fixed point Q, then the locus of the point Q for different tangents on hyperbola is an ellipse, whose length of latus rectum is

**Q.**Locus of mid point of chords of x2+y2+2gx+2fy+c=0 that pass through the origin, is

- x2+y2+2gx+2fy+c=0
- x2+y2+gx+fy+c=0
- x2+y2+gx+fy=0
- 2(x2+y2+gx+fy)+c=0

**Q.**Find the equation of the circle that passes through the points (1.0), (−1, 0) and (0, 1)

- x2−y2=1
- x2+y2=1
- None of these
- x2+y2=6

**Q.**If P(x, y, z) is a point on the line segment joining Q(2, 2, 4) and R(3, 5, 6) such that the projection of −−→OP on the axes are 135, 195, 265 respectively, then P divides QR in ratio

- 2:3
- 1:3
- 3:2
- 3:1

**Q.**If the area of the circle 4x2+4y2+8x−16y+λ=0 is 9π sq. units, then the value of λ is

- −4
- 4
- 16
- −16
- −8

**Q.**Let 3x−y−3=0 is a diameter of the circle x2+y2−4x−6y+4=0. If L1 is the chord which is bisected by the given diameter line, then which of the following is/are true?

- When L1 is the largest possible chord of the circle, its possible equation is x+3y−11=0
- When L1 is the largest possible chord of the circle, its possible equation is x−3y+8=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11+√10=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11−√10=0

**Q.**The equation of diameter which bisects the chord 3x+y+5=0 of the circle x2+y2=16 is

- 3x+y=0
- x+3y=0
- 3x−y=0
- x−3y=0

**Q.**Let 3x−y−3=0 is a diameter of the circle x2+y2−4x−6y+4=0. If L1 is the chord which is bisected by the given diameter line, then which of the following is/are true?

- When L1 is the largest possible chord of the circle, its possible equation is x+3y−11=0
- When L1 is the largest possible chord of the circle, its possible equation is x−3y+8=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11+√10=0
- When L1 is at a distance of 1 from the centre, its equation is x+3y−11−√10=0

**Q.**

Chord of contact from any point on the line x + y = 4r to the circle x2+y2=r2 (such that r>0) passes through the point (1, 1).What will be the value of r.

3

8

5

4

**Q.**The chord of the parabola y=−a2x2+5ax−4 touches the curve y=11−x at the point x=2 and is bisected by that point. Find ′a′.

**Q.**Find the scalar components and magnitude of the vector joining the points P(x1, y1, z1) and Q(x2, y2, z2).

.

**Q.**

The locus of the mid points of the chords of the circle x2+y2−ax−by=0 which subtend a right angle at (a2, b2) is :

ax+by=0

ax+by=a2+b2

x2+y2−ax−by+a2+b28=0

x2+y2−ax−by+a2+b28=0

**Q.**

The circle x2+y2−6x−4y+9=0 bisects the circumference of the circle x2+y2−(λ+4)x−(λ+2)y+(5λ+3)=0 if λ is equal to

4

-1

1

2