Question

A square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinates axes. The coordinates of its vertices are

• A. $(-6,-9),(-6,5),(8,-9)$ and $(8,5)$
• B. $(-6,9),(-6,-5),(8,-9)$ and $(8,5)$
• C. $(-6,-9),(-6,5),(8,9)$ and $(8,5)$
• D. $(-6,-9),(-6,5),(8,-9)$ and $(8,-5)$

Answer 1

The correct option is A $(-6,-9),(-6,5),(8,-9)$ and $(8,5)$

Circle: $x^2+y^2–2x+4y–93=0$

Centre: $(1,–2)$

Radius = $\sqrt{(1^2+2^2+93)}=\sqrt{\left(98\right)}$

Length of diagonal of square = diameter of circle.

Let side of square is a,

$\sqrt{(a^2+a^2)}=2\times \sqrt{\left(98\right)}$

$⟹2a^2=98\times 4$

$⟹a^2=196$

$⟹a=14$

Sides of square are parallel to the co-ordinate axes,

Distance of each side from centre is $7.$

sides parallel to y axis are $x=1+7$ and $x=1–7$

$x=8$ and $x=–6$

Also sides parallel to x axis are $y=–2+7=5$ and $y=–2–7=–9.$

Vertices of square are $(–6,–9)(–6,5)(8,–9)(8,5)$