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and the directrix with the equation 
.
lies on the directrix of a given parabola.
and passes through the origin.
and 
.
:
. Draw the concentric circles.
, a circle 
and foci on the abscissa.
and 
.
and 
are given. Write the equation of a circle with diameter 
.
runs through two vertex ellipses in the central position.
.
represents a circle?
. Obtain the equation of the hyperbola, the coordinates of all its characteristic points, and the equation of asymptotes.
, 
and 
.
passes through points 
and 
. Obtain the coordinates of the centre, radius and equation the circle.
. Also determine the coordinates of its centre.
is given. Obtain the vertices, coordinates of the centre, foci and the equation of asymptotes of the hyperbola.
with the ellipse 
.
and 
.
so that the line will be a tangent to the circle 
.
and goes through the point 
.
and the asymptotes 
.
, touches the ordinate axis, and has a radius of 
.
is given. Obtain the coordinates of the vertex of the triangle enclosed by the coordinate axes and the tangent to the function f at the point 
.
and 
, and its pole on the ordinate axis measures 6 units. Draw an ellipse and write down the foci.
, and the lines 
and 
are its asymptotes.
and 
.
and 
.
with the coordinate axes. Also determine the asymptote equations.
, calculate the intersection of the curve with the coordinate axes and draw the curve in the coordinate system.
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 the semi major axis measures 2 units. Determine the equations of the asymptotes and draw the hyperbola.
, 
, 
and 
. For each of the circles, write the centre, radius, and equation of the circles.
and 
are vertices of the rectangle.
.
,
.
.
and 
and passes through the point 
. Write down its equation and the other two coordinates.
with the axis x, and one focus is at the point 
. Write down its asymptotes as well. What angle do the asymptotes enclose with the abscissa?
is tangent to the circle 
.
in parallel so that its centre is in the coordinate origin. Obtain the coordinates of the foci and the asymptote equation of the resulting hyperbola.
and 
, and passes through the point 
.
and has a tangent 
.
and 
is drawn in the plane.
and goes through the point 
.
and 
.
(also draw the asymptotes). Calculate and obtain the intersections of the hyperbola and the line 
.
.
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.
and 
are given. Write the equation of a circle with radius 
.
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.
is a circle. Hence, draw the circle.
if it intersects the y-axis on its chord which measures 
.
and the parabola 
.
and 
.
intersects the circle 
. Calculate the length of the common chord.
, 
and 
with respect to the circle 
?
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 the ends of the diameter are on the coordinate axes.
and 
.
and the circle 
.
and 
.
and has a centre at the point 
.
in the coordinate system.
lies on the given circle.
, which has its centre at the focus 
of the ellipse with equation 
.
and the parabola 
.
passes through the points 
and 
, and its centre lies on the line 
.
on the circle 
is equal to 
.
with base 
should be inscribed on the plane 
should lie in the first quadrant on the line 
. Write the vertices 
and calculate the area of the trapezium 
.
and 
. Calculate the area of the red shaded part between the curves. The result should be accurate.
.
.
