Question

The set of points on the axis of the parabola $2\left\{\right(x-1{)}^2+(y-1{)}^2\}=(x+y{)}^2$ from which three distinct normals can be drawn is the set of points $(h,k)$ lying on the axis of the parabola, such that

• A. $h>\frac{3}{2}$
• B. $h>2$
• C. $h>4$
• D. $k<\frac{3}{2}$

Answer 1

Answer: (A)

$h>\frac{3}{2}$

$(x-1{)}^2+(y-1{)}^2={\left(\frac{x+y}{\sqrt{2}}\right)}^2$ is equation of parabola
$\Rightarrow$ Focus $=(1,1)$

$\therefore$ Vertex $=(\frac{1}{2},\frac{1}{2})$ for three normals to exist $h>3a$

$\Rightarrow h>3\left(\frac{1}{2}\right)=h>\frac{3}{2}$

Hence, option A.