Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
22 Cards in this Set
- Front
- Back
- 3rd side (hint)
|
Circle |
A circle is the locus of a point which moves in such a way that its distance from a fixed point is constant. |
Locus point |
|
|
Necessary and sufficient condition for ax2+by2+2hxy+2gx+2fy+c=0. To represent a circle. |
1). Coefficient of x2=coefficient of y2 2). h=0 3). r=underroot g2+f2-c should be defined |
|
|
|
Equation of chord of contact whose midpoint is (x1,y1) |
It has 2 equations 1). xx1 + yy1 minus a square = x1 square + y1 square minus a square. 2). T=s1 Both are the equations of line AB. |
|
|
|
Equation of chord of contact whose external point coordinates are given. |
It is defined as straight line joining the point of contact of a pair of tangent drawn from an external point (x1,y1) its equation is given by- Xx1+yy1=a square |
|
|
|
Equation of pair of tangents |
Ss1=t square |
|
|
|
Director circle |
The locus of point of intersection of two mutually perpendiculars drawn from external point to a given circle is called director of circle. X square + y square = 2 a square. |
|
|
|
Normal of a circle passing through given point |
Standard Circle - y1x minus x1y = 0 General circle - (y+f) by (x+g) = ( y1+f ) by (x1 + g ) |
|
|
|
What is Cartesian form equation of a a pair of tangents. |
When the point of contact of tangent is given Then equation of the pair of tangent is xx1+yy1=a square |
|
|
|
List three ways in which tangents can be founded |
1). Cartisan form 2).slope form 3). Parmetric form |
|
|
|
Parametric form equation |
X cos theta +y sine theta = a |
|
|
|
Slope form equation of the pair of tangent |
Y= mx+minus a under root 1+ m square |
|
|
|
What is the coordinates of point of contact |
Minus a square m by c, a square by c |
|
|
|
Equation of tangent to the second degree of curve |
S1=0 |
|
|
|
How we can say about the position of a point with respect to a circle |
S1>=or<0 then the point lies outside, on or inside a circle |
|
|
|
Equation of tangent to the circle s=0 at (x1,y1) is |
xx1+yy1+g(x+x1)+f(y+y1)+c=0 |
|
|
|
The conditions that the straight line y=mx+c is a tangent to a standard circle is x square |
C square = a square (1+m square) |
|
|
|
Length of tangent from an external point (x1,y1) is |
root s1=0 |
|
|
|
Equation of chord from an external point (x1,y1) |
T=0 |
|
|
|
What is radical axis of the two circles |
It is the locus of a point from which tangent segments to the two circles are of equal lengths. |
|
|
|
Equation of the radical axis |
S minus s dash |
|
|
|
What are the two ways in which radical axis be |
Common Tangent if they touch each other Common chord if both intersect each other |
|
|
|
Properties of radical axis |
It is perpendicular to the line joining the centres The radical axis of three circles taken two at a time are concurrent and point of concurrency is known as radical centre. The radical axis of two circle bisects their common tangents. If two circles cut each other orthogonally then the radical axis of the two circles will pass through the centre of the third circle |
|
