Circle Flashcards
x,y intercept of circles
The parametric coordinates of points at ends of diameter of a circle is
(r cosθ, r sinθ)
-r cosθ, -r sinθ
How to find if a line touches a circle
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
equation of normal to circle formula and how will we generally find the formula
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
equation of circle with end points of diameter given
Tangent of circle equation
poinit of contact of tangents on the circle iwith the radius ad slope of tangent given
Parametric points of a circle
(r cosθ, r sinθ)
Normal of a circle passes through which point
centre of the circle
Whats a director circle and whats the equation of director circle of a circle with radius r
A circle consisting of all points where two perpendicular tangent lines to the circle cross each other is called director circle
length of tangent from a point to the circle formula
Pair of tangent equation
Chord of contact equation
How will we find the length of chord of contact with given lenthg of chord and radius of circle
chord of contact if midpoint is given of the chord
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?
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
What do to if we have two circles and we want to find if they meet or not
find radius of one circle! radius of other and the distance between the circles’ centre
Angle between 2 circles formula
d is the distance between the centres
equation of common chord of two intersecting circles
Orthogonal circle condition
Radical axis equation
What is a radical axis
a straight line that is the locus of points from which tangents drawn to two given circles are equal
The radical axis is perpendicular to which line and bisects which line
its perpendicular to the line joining the centres and it bisects the same line
Family of lines for 2 intersecting cirfcles
Length of chord formula
family of lines for a circle and a line intersecing it at 2 points
family of lines for a circle with given points of diameter
family of lines for a circle touching a fixed line
position of two circles relations
