Question

The line segment joining (5,0) and (10 cos t, 10 sin t) is divided internally in the ratio 2:3 at P. If t varies, then the locus of P is

• A. a straight line
• B. a circle
• C. an ellipse
• D. a hyperbola

Answer 1

The correct option is B

a circle

P(x,y) divides the line segment joining (5,0) and (10 cos t, 10 sin t) internally in the ratio 2:3
$\therefore x=\frac{2\times 10cost+3\times 5}{2+3}x=4cost+3y=\frac{2\times 10sint+3\times 0}{2+3}y=4sint$

$(x-3{)}^2+y^2=16co{s}^{2}t+16si{n}^{2}t\Rightarrow (x-3{)}^2+y^2=16$

The above equation represents a circle