I If a point `(alpha, beta)` lies on the circle `x^2 +y^2=1` then the locus of the point `(3alpha.+2, beta),` is

Options

A. a straight line
B. an ellipse
C. a parabola
D. none of these

Answer

B

Explanation

Let `h=3 alpha + 2` and `k=beta`. Then,
`alpha=(h-2)/(3)` and `beta=k`
`:' (alpha, beta) ` lies on the circle `x^(2)+y^(2)=1`
`:. alpha^(2) +beta^(2)=1 rArr ((h-2)/(3))^(2)+k^(2)=1`
Hence, locus of (h, k) is `((x-2)^(2))/(9)+y^(2)=1` , which is an ellipse.