A square is inscribed in the circle x^{2} + y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given circle is $x^{2} + y^{2} - 2x + 4y - 93 = 0$.Completing the square,we get $(x - 1)^{2} + (y + 2)^{2} = 93 + 1 + 4 = 98$.The center is $(

Vedclass · Accepted Answer

$(-6, -9), (-6, 5), (8, -9), (8, 5)$

Vedclass · Answer

(C) The given circle is $x^{2} + y^{2} - 2x + 4y - 93 = 0$.Completing the square,we get $(x - 1)^{2} + (y + 2)^{2} = 93 + 1 + 4 = 98$.The center is $(1, -2)$ and the radius $R = \sqrt{98} = 7\sqrt{2}$.Let the side length of the square be $s$. Since the sides are parallel to the axes,the distance from the center $(1, -2)$ to each side is $s/2$.The distance from the center to a vertex is the radius $R = 7\sqrt{2}$.In a square with sides parallel to the axes,the distance from the center to a vertex is $\sqrt{(s/2)^{2} + (s/2)^{2}} = \frac{s}{\sqrt{2}}$.Equating this to the radius: $\frac{s}{\sqrt{2}} = 7\sqrt{2} \Rightarrow s = 14$.The sides are at distance $s/2 = 7$ from the center $(1, -2)$.The vertical sides are $x = 1 \pm 7$,i.e.,$x = -6$ and $x = 8$.The horizontal sides are $y = -2 \pm 7$,i.e.,$y = -9$ and $y = 5$.Thus,the vertices are $(-6, -9), (-6, 5), (8, -9), (8, 5)$.

Column-$I$	Column-$II$
$(A)$ Blue-green algae	$(i)$ Spirogyra
$(B)$ Unicellular algae	$(ii)$ Nostoc
$(C)$ Filamentous algae	$(iii)$ Volvox
$(D)$ Colonial algae	$(iv)$ Chlamydomonas

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

Similar Questions

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force will now be

In which one of the following do male and female gametophytes not have a free-living independent existence?

Match the following columns:
Column-$I$ Column-$II$
$(A)$ Blue-green algae $(i)$ Spirogyra
$(B)$ Unicellular algae $(ii)$ Nostoc
$(C)$ Filamentous algae $(iii)$ Volvox
$(D)$ Colonial algae $(iv)$ Chlamydomonas

An air bubble of radius $1 \ cm$ rises from the bottom portion through a liquid of density $1.5 \ g/cc$ at a constant speed of $0.25 \ cm/s$. If the density of air is neglected,the coefficient of viscosity of the liquid is approximately,(in $Pa \cdot s$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module