For an ellipse having major and minor axis along `x` and `y` axes respectivley, the product of semi major and semi minor axis is `20`. Then maximum value of product of abscissa and ordinate of any point on the ellipse is greater than (A) `5` (B) `8` (C) `10` (D) `15`

Options

A. `5`
B. `8`
C. `10`
D. `15`

Answer

A, B

Explanation

Equation of ellipse is `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
For any point `(x_(1),y_(1))` on the curve
`((x^(2))/(a^(2))+(y^(2))/(b^(2)))/2gesqrt((x_(1)^(2)y_(1)^(2))/(a^(2)b^(2)))implies1/2ge(x_(1)y_(1))/(ab)impliesx_(1)y_(1)le(ab)/2`
`impliesx_(1)y_(1)le10`
Which is greater than `5` and `8`