A square is inscribed in the circle $$x2+y2$$−$$2x+4y$$−$$93=0with$$ its sides parallel to the coordinate axes. The coordinates of its vertices, are

Question

A square is inscribed in the circle $$x2+y2$$−$$2x+4y$$−$$93=0with$$ its sides parallel to the coordinate axes. The coordinates of its vertices, are

Infinity Learn · Accepted Answer

Let $$x=a$$,$$x=b$$,$$y=c$$,$$y=d$$ be the sides of the square. The length of each diagonal of the square is equal to the diameter of the circle ∴  Diagonal $$=21+4+93=142Let$$  I be the length of each side of the square. Then,  $$2I2=($$ Diagonal $$)2$$⇒$$2l2=(142)2$$⇒$$l=14$$ .Therefore, each side of the square is at a distance $$7$$ from the centre  (1$$, $$-$$ $$2) of the given circle. This implies that  $$a=$$−$$6$$,$$b=8$$,$$c=$$−$$9$$,$$d=5Hence$$, the vertices of the square are $$(-6$$,$$-9)$$, $$(-6$$,$$5)$$, (8$$,$$-9), (8$$, $$5).

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A square is inscribed in the circle x2+y2−2x+4y−93=0with its sides parallel to the coordinate axes. The coordinates of its vertices, are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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