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The straight line (x)/(4)+(y)/(3) =1 int...

The straight line `(x)/(4)+(y)/(3) =1` intersects the ellipse `(x^(2))/(16)+(y^(2))/(9) =1` at two points A and B, there is a point P on this ellipse such that the area of `DeltaPAB` is equal to `6(sqrt(2)-1)`. Then the number of such points (P) is/are

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
Let the perpendicular distance of P from the line be h,

`:. (1)/(2) xx h xx 5 = 6 (sqrt(2)-1)`
`:. h = (12)/(5) (sqrt(2)-1)`
Also tangent parallel to the given line is `4y + 3x = 12 sqrt(2)`
Its distance from the line `4y +3x = 12` is `h =(12)/(5) (sqrt(2)-1)` Hence there are three points as shown in the figure.
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