Question

The sum of intercepts on co-ordinate axes made by the tangent to the curve `sqrtx + sqrty = sqrta` is ______

Options

• a

• 2a

• `2sqrta`

• None of these

Answer 1

The sum of intercepts on co-ordinate axes made by the tangent to the curve `sqrtx + sqrty = sqrta` is a.

Explanation:

`sqrtx + sqrty = sqrta`

∴ `1/(2sqrtx) + 1/(2sqrty).dy/dx = 0`

∴ `dy/dx = -sqrty/sqrtx`

∴ Equation of the tangent at (x, y) is

Y - y = `-sqrty/sqrtx(X - x)`

∴ `Xsqrty + Ysqrtx = sqrt(xy)(sqrtx + sqrty)`

∴ `Xsqrty + Ysqrtx = sqrt(xy).sqrta`

∴ `X/(sqrtasqrtx) + Y/(sqrtasqrty) = 1`

Clearly, its intercepts on the axes are `sqrta sqrtx` and `sqrta sqrty`.

Sum of the intercepts

= `sqrta(sqrtx + sqrty) = sqrta. sqrta = a`