# Length of Intercept Made by a Circle on a Straight Line

## Trending Questions

**Q.**px+qy=40 is a chord of minimum length of the circle (x−10)2+(y−20)2=729. If the chord passes through (5, 15), then p2019+q2019 is equal to

- 0
- 2
- 22019
- 22020

**Q.**If a chord of the circle x2+y2=8 makes equal intercepts a on the coordinate axes, then

- |a|<2
- |a|≤2√2
- |a|<4
- |a|<√2

**Q.**The sum of the squares of the lengths of the chords intercepted on the circle, x2+y2=16 by the lines, x+y=n ;n∈N, where N is the set of all the natural numbers, is :

- 105
- 210
- 320
- 160

**Q.**

The locus of the centre of the circle, which cuts the circle ${x}^{2}+{y}^{2}-20x+4=0$ orthogonally and touches the line $x=2$, is

${x}^{2}=16y$

${y}^{2}=4x$

${y}^{2}=16x$

${x}^{2}=4y$

**Q.**Two chords are drawn from the point P(h, k) on the circles x2+y2−hx−ky=0. If the y-axis divides both the chords in the ratio 1:3, then which of the following is/are correct?

- 9k2>16h2
- k2>48h2
- 9k2≥16h2
- 4k2=h2

**Q.**

The product of the length of the perpendiculars drawn from the point (1, 1) to the pair of lines x^2 + xy - 6y^2 = 0 is?

**Q.**The equation of the circle which is touched by y=x, has its centre on the positive direction of the x-axis and cuts off a chord of length 2 units along the line √3y−x=0, is

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

**Q.**The shaded region shown in the figure is given by the inequation

- 14x+5y≥70 y≤14 and x−y≤5
- 14x+5y≥70 y≤14 and x−y≥5
- 14x+5y≤70 y≤14 and x−y≥5
- 14x+5y≥70 y≥14 and x−y≥5

**Q.**

Choose the incorrect statement about the two circles whose equations are given below:

${x}^{2}+{y}^{2}\u201310x\u201310y+41=0$and ${x}^{2}+{y}^{2}\u201316x\u201310y+80=0$.

Distance between two centers is the average radii of both the circles.

Circles have two intersection points.

Both circles’ centers lie inside the region of one another.

Both circles pass through the center of each other.

**Q.**The equation of a line inclined at an angle π4 to the x−axis, such that the two circles x2+y2=4, x2+y2−10x−14y+65=0 intercept equal lengths on it, is

- 2x−2y+3=0
- 2x−2y−3=0
- x−y−6=0
- x−y+6=0

**Q.**

If the lengths of the tangents from the point (1, 2) to the circles x2+y2+x+y−4=0 and 3x2+3y2−x−y−λ=0 are in the ratio 4:3 then λ=

**Q.**

What is the equation of the chord of the circle ${x}^{2}+{y}^{2}=81$ which is bisected at point $\left(-2,3\right)$ ?

$3x-y=13$

$3x-4y=13$

$2x-3y=13$

$3x-3y=13$

$2x-3y=-13$

**Q.**

**Q.**The value of |c| for which the set {(x, y):x2+y2+2x≤1}∪{(x, y):x−y+c≥0} contains only one point is equal to

**Q.**Which of the following lines have the intercepts of equal lengths made by the circle x2+y2−2x+4y=0 is/are

- 3x−y=0
- x+3y=0
- x+3y+10=0
- 3x−y−10=0

**Q.**

Let P and Q be two points denoting the complex numbers α and β respectively on the complex plane. Which of the following equations can represent the equation of the circle passing through P and Q with least possible area ?

- arg(z−αz−β)=π2
- Re(z−α)(¯¯¯¯¯¯¯¯¯¯¯¯z−β)=0
- |z−α|2+|z−β|2=(¯¯¯¯¯¯¯¯¯¯¯¯¯α−β)2
- z¯z+(¯α+¯β2)z+(α+β2)¯z+α¯β+¯αβ=0

**Q.**The equation of circle passing through the origin and cutting off equal intercepts of 2 units on the lines √3y2−√3x2−2xy=0 is/are

- (x+√3)(x−1)+(y−√3)(y−1)=0
- (x+1)(x+√3)+(y+√3)(y−1)=0
- (x−√3)(x+1)+(y+1)(y+√3)=0
- (x−√3)(x−1)+(y+1)(y−√3)=0

**Q.**

The lines ax2+2hxy+by2=0 are equally inclined to the lines

ax2+2hxy+by2+λ(x2+y2)=0 for

= 1 only

= 2 only

for any value of

None of these

**Q.**The number of integral values of k for which the chord of the circle x2+y2=125 passing through P(8, k) gets bisected at P(8, k) and has integral slope, is

**Q.**The equation of a line parallel to the line 3x+4y=0 and touching the circle x2+y2=9 in the first quadrant is

- 3x+4y=15
- 3x+4y=45
- 3x+4y=9
- 3x+4y=27

**Q.**

Let P, Q, R, S and T are five sets about the quadratic equation

(a – 5)x2 – 2ax + (a – 4) = 0, a ≠ 5 such that

P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.

Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.

R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.

S : All values of ‘a’ for which the roots of given quadratic are real.

T : All values of ‘a’ for which the given quadratic equation has complex roots.

none of the above.

least positive integer for set R is 2

greatest positive integer for set T is 3

least positive integer for set R is 3

**Q.**

A line having slope 1 is drawn from a point A (-3, 0) cuts a curve y=xx^{}^{2}+x+1 at P and Q . Find l(AP) and l(AQ).

**Q.**The equation of the circle which is touched by y=x, has its centre on the positive direction of the x-axis and cuts off a chord of length 2 units along the line √3y−x=0, is

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

**Q.**

Write the length of the intercept made oy the circle x2+Y2+2x−4y−5=0

on y-axis.

**Q.**

Using the method of integration find the area of the region bounded by lines:

2*x* + *y* =
4, 3*x* – 2*y* = 6 and *x* – 3*y *+ 5
= 0

**Q.**

Let L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by

the circle x2+y2−x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1

x + y = 0

x - y = 0

x + 7y = 0

x - 7y = 0

**Q.**

Find the equation of chord centered at the point (1, 2) in the circle x2 + y2 = 9.

x + 2y - 5 = 0

x - 2y + 5 = 0

x + 2y + 5 = 0

x - 2y - 5 = 0

**Q.**

The number of straight lines that are equally inclined to the three-dimensional co-ordinate axis, is

$2$

$4$

$6$

$8$

**Q.**

Let L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by

the circle x2+y2−x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1

x + y = 0

x - y = 0

x + 7y = 0

x - 7y = 0

**Q.**

The length of the chord intercepted by the circle x2+y2=r2 on the line xa+yb=1

√r2(a2+b2)−a2b2a2+b2

2√r2(a2+b2)−a2b2a2+b2

2√r2(a2+b2)−a2b2a2+b2

2√r2(a2+b2)+a2b2a2+b2