Circle

Question 1

x,y intercept of circles

Answer 1

Question 2

The parametric coordinates of points at ends of diameter of a circle is

Answer 2

(r cosθ, r sinθ)

-r cosθ, -r sinθ

Question 3

How to find if a line touches a circle

Answer 3

if the perpendicular distance of the center of the circle to the line is equal to the radius of the circle

And the following condition

Question 4

equation of normal to circle formula and how will we generally find the formula

Answer 4

generally, the equation would be found by finding the slope of normal by the slope of the tangent at the point we have to find the normal and then sub in the line equation as we have the point and the slope

Question 5

equation of circle with end points of diameter given

Answer 5

Question 6

Tangent of circle equation

Answer 6

Question 7

poinit of contact of tangents on the circle iwith the radius ad slope of tangent given

Answer 7

Question 8

Parametric points of a circle

Answer 8

(r cosθ, r sinθ)

Question 9

Normal of a circle passes through which point

Answer 9

centre of the circle

Question 10

Whats a director circle and whats the equation of director circle of a circle with radius r

Answer 10

A circle consisting of all points where two perpendicular tangent lines to the circle cross each other is called director circle

Question 11

length of tangent from a point to the circle formula

Answer 11

Question 12

Pair of tangent equation

Answer 12

Question 13

Chord of contact equation

Answer 13

Question 14

How will we find the length of chord of contact with given lenthg of chord and radius of circle

Answer 14

Question 15

chord of contact if midpoint is given of the chord

Answer 15

Question 16

what points are in the same circle in a the condition of pair of tangents from a point to a circle

and the equation of circle is?

Answer 16

the point from where the tangents are drawn and the point of intersection and the center of the circle lie in a circle with the point of tangents and center of circle being the diameter

Question 17

What do to if we have two circles and we want to find if they meet or not

Answer 17

find radius of one circle! radius of other and the distance between the circles’ centre

Question 18

Angle between 2 circles formula

Answer 18

d is the distance between the centres

Question 19

equation of common chord of two intersecting circles

Answer 19

Question 20

Orthogonal circle condition

Answer 20

Question 21

Radical axis equation

Answer 21

Question 22

What is a radical axis

Answer 22

a straight line that is the locus of points from which tangents drawn to two given circles are equal

Question 23

The radical axis is perpendicular to which line and bisects which line

Answer 23

its perpendicular to the line joining the centres and it bisects the same line

Question 24

Family of lines for 2 intersecting cirfcles

Answer 24

Question 25

Length of chord formula

Answer 25

Question 26

family of lines for a circle and a line intersecing it at 2 points

Answer 26

Question 27

family of lines for a circle with given points of diameter

Answer 27

Question 28

family of lines for a circle touching a fixed line

Answer 28

Question 29

position of two circles relations

Answer 29