VITEEE 2013 Paper

Let P(x1,y1) be a point on the ellipse

x2

18

+

y2

32

= 1
⇒

x12

18

+

y12

32

= 1 ... (i)
The equation of the tangent at (x1,y1) is

xx1

18

+

yy1

32

= 1. This meets the axes at A (

18

x1

,0) and B (0,

32

y1

). It is given that slope of the tangent at (x1,y1) is -

4

3

So , −

x1

18

.

32

y1

= -

4

3

⇒

x1

y1

=

3

4

⇒

x1

3

=

y1

4

= K (say)
∴ x1 = 3K and y1 = 4K
Putting x1,y1 in (i), we get
K2 = 1
∴ Area of Δ OAB =

1

2

OA . OB
=

1

2

.

18

x1

.

32

y1

=

1

2

(18)(32)

(3K)(4K)

=

24

K2

= 24 sq units (Since K2 =1)