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Cosine Rule

If P(at^2,2at...

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If P(at^2,2at),Q(a/t^2,-2a/t)andS(a,0)be any three points,show that1/SP+1/SQ is independent of t?

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P

Q

are two points whose coordinates are

(a t^{2}, 2 a t)

(\frac{a}{t^{2}}, - \frac{2 a}{t})

respectively and

S

(a, 0)

\frac{1}{S P} + \frac{1}{S Q}

is independent of

t

P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)

be three points on a parabola

y^{2} = 4 a x .

P Q

is the focal chord and

P K, Q R

are parallel where the co-ordinates of

K

(2 a, 0),

then the value of

r

P, Q are two points whose coordinates are

(a t^{2}, 2 a t)

(\frac{a}{t^{2}}, \frac{- 2 a}{t})

and S is a point whose coordinates is

(a, 0)

\frac{1}{S P} + \frac{1}{S Q}

is constant for all values of

t

a, r, s, t

be nonzero real numbers. Let

P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r) and S (a s^{2}, 2 a s)

be distinct points on the parabola

y^{2} = 4 a x

P Q

is the focal chord and lines

Q R

P K

are parallel, where

K

(2 a, 0) .

r

a, r, s

t

be non –zero real numbers. Let

P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)

S (a s^{2}, 2 a s)

be distinct points on the parabola

y^{2} = 4 a x

P Q

is the focal chord and lines

Q R

P K

are parallel, where

K

(2 a, 0)

r

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