If `x/alpha+y/beta=1` touches the circle `x^2+y^2=a^2` then point `(1/alpha , 1/beta)` lies on (a) straight line (b) circle (c) parabola (d) ellipse

Options

A. a straight line
B. a circle
C. a parabola
D. an ellipse

Answer

B

Explanation

If `(x)/(alpha)+(y)/(beta)=1` touches the circle `x^(2)+y^(2)=a^(2)`, then

`|((0)/(alpha)+(0)/(beta))/(sqrt((1)/(alpha^(2))+(1)/(beta^(2))))|=arArr (1)/(alpha^(2))+(1)/(beta^(2))=(1)/(a^(2))`
`rArr((1)/(alpha),(1)/(beta))` lies on `x^(2)+y^(2)=(1)/(a^(2))`, which represents a circle.