equation of : p x y · locus 36 mathematics / parabola y ax equation of : p x y y ax normalat p(x...

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LOCUS LOCUS LOCUS LOCUS LOCUS 36 Mathematics / Parabola y ax EQUATION OF : Px y y ax NORMALAT P(x 1 , y 1 ) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at 2 ,2at) at at x y at y at x at a y tx at at m t EQUATION OF : t m NORMAL WITH y mx am am SLOPE m y mx am am at at m am am Section - 3 NORMALS

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Page 1: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 36

Mathematics / Parabola

y ax

EQUATION OF : P x y y axNORMALAT P(x1, y1) P

Tx y

dy amdx y

Nyma

x y

yy y x xa

EQUATION OF : P

NORMAL AT P(at2,2at) at atx y

aty at x ata

y tx at at

m t

EQUATION OF : t mNORMAL WITH y mx am amSLOPE m y mx am am

at at m am am

Section - 3 NORMALS

Page 2: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 37

Mathematics / Parabola

m P threeP h k m P

k mh am am

am a h m k

m m m m m mm

one three P

i iam am i

a m m m

y ax

Solution: P at att

y mx am am

P

at at m am am

m t m t

m t m mt

m t P

m

t

tP

y ax t

Example – 26

Example – 27

Page 3: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 38

Mathematics / Parabola

Solution: t

y tx at at

t at at

at at t at at

at t t a t t

t t t

t tt

t y ax

AB AB

t t y ax t t t

Solution:

t t t tt

t tt

t t t t

y t x at at

y t x at at

t at at

at at t at at

at at t at at

Example – 28

Page 4: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 39

Mathematics / Parabola

at t t a t t a t t

t t t t t

a t t t t at t at t

t t t t t t t t

t t t t t t

t t

external

y ax

Solution: A at at B at at

y

x

ABO

AB, N N C

CO

N

N

C

A at , at

B at , at

Example – 29

Page 5: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 40

Mathematics / Parabola

OA OB

OA OB

at atat at

t t

N N t

N y t x at at

N y t x at at

N N C h k CN N

h a a t t t t

a a t t

k at t t t

a t t

t t h k

k h aa a

k a h a

x y h k

y a x a

y ax

Solution: P h k

y mx am am

P h k

k mh am am

Example – 30

Page 6: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 41

Mathematics / Parabola

m m mm m m m

km m ma

kma

m h k

hk akk ka a

k k a h a

x y h k

y y a x a

Page 7: EQUATION OF : P x y · LOCUS 36 Mathematics / Parabola y ax EQUATION OF : P x y y ax NORMALAT P(x 1, y 1) P T x y dy a m dx y N y m a x y y y y x x a EQUATION OF : P NORMAL AT P(at2,2at)

LOCUSLOCUSLOCUSLOCUSLOCUS 42

Mathematics / Parabola

Q. 1 y x x y

Q. 2 P y ax A y B O OACB C

Q. 3 y ax x y

Q. 4

Q. 5

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