Question

A line of fixed length a + b moves so that its ends are always on two fixed perpendicular straight lines, then the locus of a point, which divides this line into portions of lengths a and b is a/an

• A. Ellipse
• B. Parabola
• C. Straight line
• D. None of these

Answer 1

The correct option is A Ellipse

$letP=(h,0)andQ=(0,k)$

$(x,y)=[\frac{bh}{(a+b)},\frac{ak}{(a+b)}]$

${\left(\frac{x}{b}\right)}^2+{\left(\frac{y}{a}\right)}^2=1$

$\therefore EquationofPisanellipse$