# Tangent

## Trending Questions

**Q.**

If $\left|\frac{\left(z+i\right)}{\left(z-i\right)}\right|=\sqrt{3}$, then the radius of the circle is

$\frac{2}{\sqrt{21}}$

$\frac{1}{\sqrt{21}}$

$\sqrt{3}$

$\sqrt{21}$

**Q.**

The perpendicular distance of center from tangent of the circle is equal to its radius.

True

False

**Q.**In the following question, four figures are given in which first two are related to each other in some manner. In the same manner, last two figures should also be related. Which would be the correct alternative for the fourth figure?

**Q.**If the circles x2+y2+(3+sinβ)x+(2cosα)y=0 and x2+y2+(2cosα)x+2cy=0 touch each other, then the maximum value of c is

**Q.**If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is

**Q.**If the straight line y = mx + c touches the circle x2+y2−4y=0, then the value of c will be

- 1+√1+m2
- 2(1+√1+m2)
- 1−√m2+1
- 2+√1+m2

**Q.**A circle is tangent to the x and y axes in the first quadrant at the points P and Q respectively. BC and AD are parallel tangents to the circle with slope −1. If the points A and B are on the y- axis while C and D are on the x-axis and the area of the quadrilateral ABCD is 900√2 sq. units, then the radius of the circle is

- 10
- 12
- 15
- 20

**Q.**

Circle drawn through the point (2, 0) to cut intercept of length ‘5′ units on the x-axis. If its centre lie in the first quadrant then the equation of family of such circles is

x2+y2−9x+2ky+14=0, k>0

x2+y2−9x−2ky+14=0, k>0

x2+y2−9y+2ky+14=0, k>0

3x2+3y2+27x+2ky+42=0, k>0

**Q.**Let W1 and W2 denote the circles x2+y2+10x−24y−87=0 and x2+y2−10x−24y+153=0 respectively. Let m be the smallest positive value of a for which the line y=ax contains the centre of a circle that is externally tangent to W2 and internally tangent to W1. If m2=pq, where p and q are co-prime, then the value of (p+q) is

**Q.**Tangents PA and PB are drawn to the circle (x−4)2+(y−5)2=4 from the point P on the curve y=sinx, where A and B lie on the circle. Consider the function y = f(x) represented by the locus of the centre of the circumcircle of triangle PAB, then

Range of y=f(x) is

- [−2, 1]
- [−1, 4]
- [0, 2]
- [2, 3]

**Q.**

A plane passes through (1, -2, 1) and is perpendicular to two planes 2x−2y+z=0 and x−y+2z=4, then the distance of the plane form the point (1, 2, 2) is

0

√2

1

2√2

**Q.**

Find the coordinates of the point on the curve √x+√y=4 at which tangent is equally inclined to the axes.

**Q.**The two tangents to a circle from an external point are always

Equal

Perpendicular to each other

- Parallel to each other
- None of these

**Q.**If the line lx + my = 1 be a tangent to the circle x2+y2=a2, then the locus of the point (l, m) is

A straight line

- An ellipse
A Circle

- A parabola

**Q.**Consider the relation 4l2−5m2+6l+1=0, where l, m∈R, then the line lx+my+1=0 touches a fixed circle whose centre and radius of circle are

- (2, 0), 3
- (−3, 0), √3
- (3, 0), √5
- (−2, 0), 3

**Q.**The equation of circle with centre (1, 2) and tangent x + y - 5 = 0 is

- x2+y2−2x−4y+3=0
- x2+y2+2x−4y+6=0
- x2+y2−2x−4y+8=0
- x2+y2−2x+4y+8=0

**Q.**The shortest distance between the line y=x−5 and the parabola y=x2+3x+6 is

- √2 units
- 2√2 units
- 3√2 units
- 5√2 units

**Q.**Let the abscissae of the two points P and Q be the roots of 2x2–rx+p=0 and the ordinates of P and Q be the roots of x2–sx–q=0. If the equation of the circle described on PQ as diameter is 2(x2+y2)–11x–14y–22=0, then 2r+s–2q+p is equal to

**Q.**

The foot of the perpendicular of center on a tangent and the point of contact of the tangent are same.

True

False

**Q.**

The set of values of 'c' so that the equations y=|x|+c and x2+y2−8|x|−9=0 have no solution is

(∞, −3)∪(3, ∞)

(−3, 3)

(−∞, 5√2)∪(5√(2), ∞)

5√2−4, ∞

**Q.**The equation of the circle lying in first quadrant, which touches both the coordinates axes and the distance of it's centre from origin is 2 units is

- x2+y2−2√2x−2y+2=0
- x2+y2−√2x−2√2y+2=0
- x2+y2−2x−2y+2=0
- x2+y2−2√2x−2√2y+2=0

**Q.**If a circle is inscribed in a square of side 10 , so that the circle touches the four sides of the square internally then radius of the circle is

- 10
- 5√2
- 10√2
- 5

**Q.**

The equation of the circle is** **${x}^{2}+{y}^{2}-12x+6y+20=0$**. **

What is the radius of the circle?

Enter your answer in the box. $r=$ ___ units.

**Q.**

The perpendicular distance of center from tangent of the circle is equal to its radius.

True

False

**Q.**In the figure given below, three dots are placed that represent some common regions to circle, hexagon and triangle.

Choose the correct alternative figure that contains the similar common region to that represented by dots in the given figure.

**Q.**If the straight line y = mx + c touches the circle x2+y2−4y=0, then the value of c will be

- 1+√1+m2
- 1−√m2+1
- 2(1+√1+m2)
- 2+√1+m2

**Q.**Consider the circles

S1:x2+y2−12y+35=0

S2:x2+y2−4x−4y+4=0

S1:x2+y2−9x=0

Which of the following statements is correct?

- The centres of these three circles form a right triangle.
- The length of the chord intercepted on the line y=x by S3 is 3√2.
- Equation of the tangent on circle S3=0 at the origin is y=0
- Point (4, 1) lies outside S1 but inside S2 and S3.

**Q.**If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is

- 3/2
- 3/4
- 1/10
- 1/20

**Q.**The shortest distance from the origin to a variable point on the sphere (x−2)2+(y−3)2+(z−6)2=1 is

- 5
- 6
- 7
- 8

**Q.**Consider the relation 4l2−5m2+6l+1=0, where l, m∈R, then the line lx+my+1=0 touches a fixed circle whose centre and radius of circle are

- (−3, 0), √3
- (2, 0), 3
- (3, 0), √5
- (−2, 0), 3