MATH SOLVE

5 months ago

Q:
# Find the center, vertices, and foci of the ellipse with equationx^2/144+y^2/2525 = 1

Accepted Solution

A:

x^2/144+y^2/25=1

The largest denominator is a^2 and the smallest denominator is b^2, then:

a^2=144→sqrt(a^2)=sqrt(144)→a=12

b^2=25→sqrt(b^2)=sqrt(25)→b=5

The equation is of the form:

x^2/a^2+y^2/b^2=1

This is an ellipse with center C=(h,k) at the Origin → C=(0,0) and major axis on the x-axis and minor axis on the y-axis.

The vertices have coordinates:

V'=(-a,0) and V=(a,0)

Replacing a=12

V'=(-12,0) and V=(12,0)

The foci have coordinates:

F'=(-c,0) and F=(c,0)

c^2=a^2-b^2

c^2=144-25

c^2=119

sqrt(c^2)=sqrt(119)

c=sqrt(119)

Then the coordinates of the foci are:

F'=(-sqrt(119),0) and F=(sqrt(119),0)

Answers:

Centrer: C=(0,0)

Vertices: V'=(-12,0) and V=(12,0)

Foci: F'=(-sqrt(119),0) and V=(sqrt(119),0)

The largest denominator is a^2 and the smallest denominator is b^2, then:

a^2=144→sqrt(a^2)=sqrt(144)→a=12

b^2=25→sqrt(b^2)=sqrt(25)→b=5

The equation is of the form:

x^2/a^2+y^2/b^2=1

This is an ellipse with center C=(h,k) at the Origin → C=(0,0) and major axis on the x-axis and minor axis on the y-axis.

The vertices have coordinates:

V'=(-a,0) and V=(a,0)

Replacing a=12

V'=(-12,0) and V=(12,0)

The foci have coordinates:

F'=(-c,0) and F=(c,0)

c^2=a^2-b^2

c^2=144-25

c^2=119

sqrt(c^2)=sqrt(119)

c=sqrt(119)

Then the coordinates of the foci are:

F'=(-sqrt(119),0) and F=(sqrt(119),0)

Answers:

Centrer: C=(0,0)

Vertices: V'=(-12,0) and V=(12,0)

Foci: F'=(-sqrt(119),0) and V=(sqrt(119),0)