A PROBLEM ON CONIC SECTIONS

length=12 cm

Point C at 3cm

REFRESH

A rod AB of length 12 cm rests in between two coordinate axes in such
a way that the end point A lies on x-axis and end point B lies on
y-axis. A point C(x, y) is taken on the rod in such a way
that AC = 3 cm. Show that the locus of P is an ellipse.

3 cm

Below the x axis

C

B

Instructions >>
Please click the checkbox “ Point C at 3 cm  ”
and drag the point A slowly  (on the x axis
Click the checkbox “ Below the x axis” 
to get the portion of the ellipse below
the x axis.

-benny varghese
rpo,nli goa

A Problem on Conic Sections

3 cm

A = Point(xAxis)
a: 144 - (x(A))^(2)
b: sqrt(a)
B: (0, b)
c = Segment(B, A)
d = Circle(A, 3)
C = Intersect(d, c)
e = false
D = Midpoint(A, C)
B': (0, (-b))
f = Segment(A, B')
C' = Intersect(d, f)
g = false
E = Midpoint(A, C')