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Perpendicular Distance of a Point from a Line

Let P a θ,b ...

Question

Let P $(a sec θ, b t a n θ)$ and Q $(a s e c \emptyset, b tan \emptyset)$ where $θ + \emptyset = p i / 2$ , be two points on the hyperbola $x^{2} / a^{2} -^{2} / b^{2} = 1$ . If (h,k) is the point of intersection of normals at P and Q, then k is equal to ?

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Solution

The equation of parabola is 
the equation of the normal at a point p(asecθ,btanθ) is given as 
                                     the equation of the normal at a point q(asecФ,btanФ) is given by             
                                   solving (i) and (ii) we get

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Similar questions

Q. Let P

(a s e c θ, b t a n θ)

and Q

(a s e c ϕ, b t a n ϕ)

, where

θ + ϕ = \frac{π}{2}

, be two points on the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

. If (h, k) is the point of intersection of the normals at P & Q, then k is equal to

Q. Let

P (a sec θ, b tan θ)

and

Q (a sec ϕ, b tan ϕ)

where

θ + ϕ = π / 2

, be two points on the hyperbola

x^{2} / a_{2} - y_{2} / b_{2} = 1

. If (h, k) is the point of intersection of normals at P and Q, then k is equal to

Q. Let

P (a sec θ, b tan θ)

and

Q (a sec ϕ, b tan ϕ),

where

θ + ϕ = \frac{π}{2}

, be two points on the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

. If

(h, k)

is the point of intersection of normals at

P

and

Q

, then

k

is equal to

Q. Let

P (a sec θ, b tan θ)

and

Q (a sec ϕ, b tan ϕ)

, where

θ + ϕ = \frac{π}{2}

, be two points on the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

. If

(h, k)

is the point of intersection of the normals at

P

and

Q

, then

k

is equal to

Let $P (a s e c θ, b t a n θ)$ and $Q (a s e c ϕ, b t a n ϕ)$ , where $θ + ϕ = \frac{π}{2}$ , be two points on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ .
If (h, k) is the point of the intersection of the normals at P and Q, then k is equal to

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Let P(asecθ,b tanθ)and Q(asec∅,btan∅)where θ+∅=pi/2, be two points on the hyperbola x2/a2−2/b2=1. If (h,k) is the point of intersection of normals at P and Q, then k is equal to ?

The equation of parabola is the equation of the normal at a point p(asecθ,btanθ) is given as ​ the equation of the normal at a point q(asecФ,btanФ) is given by solving (i) and (ii) we get

Let P $(a sec θ, b t a n θ)$ and Q $(a s e c \emptyset, b tan \emptyset)$ where $θ + \emptyset = p i / 2$ , be two points on the hyperbola $x^{2} / a^{2} -^{2} / b^{2} = 1$ . If (h,k) is the point of intersection of normals at P and Q, then k is equal to ?