Circles

Question 1

Diametric form

Answer 1

(x-x1)(x-x2) + (y-y1)(y-y2) = 0

Question 2

r =

Answer 2

√g^2 + f^2 - C

Question 3

Power of a pt

Answer 3

S1 = x1^2 + y1^2 + 2gx1 + 2fy1 + C

Question 4

If S1 > 0

Answer 4

pt lies out

Question 5

Length of tangent

Answer 5

√S1

Question 6

Intercept cut off by circle from x axis

Answer 6

2√g^2-C^2

Question 7

Eqn of line

Answer 7

lx + my + n = 0

Question 8

If r1+r2 < C1C2

Answer 8

circles don’t touch

Question 9

If r1+r2>C1C2

Answer 9

Circles touch externally

Question 10

If r1 + r2 = C1C2

Answer 10

Circles intersect at 2 pts

Question 11

If r1-r2 = C1C2

Answer 11

Circles touch internally

Question 12

If r1-r2 < C1C2

Answer 12

One circle in other

Question 13

Common chord eqn

Answer 13

S1 - S2 = 0

Question 14

director circle

Answer 14

x^2+y^2 = 2r^2

Question 15

angle b/n circles cos(180-θ) =

Answer 15

[r1^2 + r2^2 - (C1C2)^2]/2r1r2

Question 16

If 2 circles cut orthogonally

Answer 16

r1^2 + r2^2 = (C1C2)^2

Question 17

No of common tangents

Answer 17

4 if they don’t touch
3 if they touch
2 if they intersect at 2 pts
1 if one is in other & touches
0 if one in other

Question 18

Eqn of tangent to circle

Answer 18

xx1 + yy1 = r^2

Question 19

Condition for line to be tangent to x^2 + y^2 = r^2

Answer 19

C^2 = r^2(1+m^2)

Question 20

Parametric eqns

Answer 20

x = rcosθ
y = rsinθ

Question 21

If e = 0

Answer 21

circle

Question 22

If e = 1

Answer 22

parabola

Question 23

if e < 1

Answer 23

ellipse

Question 24

For y^2 = 4ax

Answer 24

focus(a,0)
directrix x = -a
LR = 4a
focal dist = |x+a|

Question 25

Parametric form for y^2 = 4ax

Answer 25

x = at^2, y = 2at

Question 26

For x^2 = 4ay

Answer 26

Focus(0,a) directrix y = -a LR = 4a Focal dist |y+a|

Question 27

Parametric form for x^2=4ay

Answer 27

x = 2at, y = at^2

Question 28

Shift of vertex

Answer 28

(x-h)^2 = 4a(y-k)

Question 29

Point of contact for y^2=4ax

Answer 29

x = a/m^2 , y = 2a/m

Question 30

Point of contact for x^2=4ay

Answer 30

x = 2am, y = am^2

Question 31

Eqn of tangent at (x1,y1) to y^2=4ax

Answer 31

yy1 = 2a(x+x1)

Question 32

Eqn of normal at (x1,y1) to y^2=4ax

Answer 32

y-y1 = -y1(x+x1)/2a

Question 33

For ellipse

Answer 33

Foci(a,0) e = c/a x = +-a/e LR = 2b^2/a c = √a^2-b^2

Question 34

For ellipse, eqn of tangent

Answer 34

y = mx +- √a^2m^2+b^2 or mx +- √b^2m^2+a^2

Question 35

Pt of contact for ellipse

Answer 35

-a^2m/c , b^2/c

Question 36

auxillary circle

Answer 36

x^2 + y^2 = a^2

Question 37

director circle for ellipse

Answer 37

x^2 + y^2 = a^2 + b^2

Question 38

For hyperbola, eqn of tangent

Answer 38

C^2 = a^2m^2 - b^2

Question 39

For hyperbola, pt of contact

Answer 39

+-a^2m/c, b^2/c

Question 40

Director circle for hyperbola

Answer 40

x^2+y^2 = a^2 - b^2

Question 41

In rectangular hyperbola, e =

Answer 41

√2