You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of Normal at Given Point

The variable ...

Question

The variable line drawn through the point $(1, 3)$ meets the $x$ -axis at $A$ and $y$ -axis at $B$ . If the rectangle $O A P B$ is completed. Where $O$ is the origin, then locus of $" P "$ is

\frac{1}{y} + \frac{3}{x} = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x + 3 y = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{x} + \frac{3}{y} = 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 x + y = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $\frac{1}{x} + \frac{3}{y} = 1$
The coordinates of A is in the form $(h, o) a n d t h a t o f B i s (o, k)$ $
Slope of line AB = $\frac{0 - 3}{h - 1} = \frac{3}{1 - h}$ $\to$ (1)

Slope of line AB = $\frac{3 - k}{1 - 0}$ $\to$ (2)

Comparing equation 1 and 2

$\Rightarrow \frac{3}{1 - h} = \frac{3 - k}{1}$

$\Rightarrow (1 - h) (3 - k) = 3$ [ $∵$ where $k = y, h = x$ ]
$3 - k - 3 h + h k = 3$
$\Rightarrow - k - 3 h + h k = 0$
$∴ 3 x + y - x y = 0 \Rightarrow \frac{1}{x} + \frac{3}{y} = 1$ [dividing through out by $x y$ ]

Suggest Corrections

Similar questions

Q. A variable line passes through a fixed point

(x_{1}, y_{1})

and meets the axes at

A

and

B

. If the rectangle

O A P B

be completed, the locus of P is, (

O

being the origin of the system of axes)

Tangent at any point on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ cut the axis at A and B respectively. If the rectangle OAPB (where O is origin) is completed then locus of point P is given by

Q. The foot of the perpendicular drawn from the origin, on the line,

3 x + y = λ (λ \neq 0)

P

. If the line meets

x

-axis at

A

and

y

-axis at

B

, then the ratio

B P : P A

is :

Q. A variable line

L

is drawn through

O (0, 0)

to meet

L_{1} : x - y - 8 = 0

and

L_{2} : x - y - 16 = 0

at points

A

and

B

respectively. A point

P

is taken on

L

such that

\frac{1}{4 O P} = \frac{1}{O A} + \frac{1}{O B}

. Then the locus of

P

Q. A tangent to the curve,

y = f (x)

P (x, y)

meets

x -

axis at

A

and

y -

axis at

B

. If

A P : B P = 1 : 3

and

f (1) = 1

, then the curve also passes through the point.

Join BYJU'S Learning Program

The variable line drawn through the point (1,3) meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed. Where O is the origin, then locus of "P" is

The variable line drawn through the point $(1, 3)$ meets the $x$ -axis at $A$ and $y$ -axis at $B$ . If the rectangle $O A P B$ is completed. Where $O$ is the origin, then locus of $" P "$ is