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and 
.
, a circle 
and foci on the abscissa.
runs through two vertex ellipses in the central position.
. Also determine the coordinates of its centre.
with the ellipse 
.
and goes through the point 
.
and 
, and its pole on the ordinate axis measures 6 units. Draw an ellipse and write down the foci.
and 
.
and 
. Write down the coordinates of the foci of this ellipse. Also write down the equation of a circle that has a centre at the point 
and passes through the origin of the coordinate system.
and 
are vertices of the rectangle.
.
,
.
and 
and passes through the point 
. Write down its equation and the other two coordinates.
and 
is drawn in the plane.
in the given coordinate system. Write down the foci of the ellipse. Write down the equation of the circle centered at the right vertex of the given ellipse and touching the ordinate axis.
touches the ordinate axis and it also cuts off a distance of length 4 on the abscissa axis. Calculate the semi-axis of the ellipse and write down its equation. Also draw a sketch and ensure the results are accurate.
and the parabola 
.
intersects the circle 
. Calculate the length of the common chord.
and a parabola 
. Calculate the area of the quadrilateral whose vertices are the intersections of the circle with the abscissa and with the parabola.
and 
.
and 
.
and the parabola 
.
