The distance between the directrix and the focus of a parabola is 50 mm. Draw the curve. Draw a tangent and normal at a point of the curve 100 mm from the directrix.
A stone thrown from the ground reaches a maximum height of 40 mm falls on to the ground at a distance of 100 m from the point of projection. Trace the path of the stone in space.
A stone is thrown from a 7 m high building, and at its highest flight the stone just crosses a 14 m high palm tree. Trace the path of the stone till it touches the ground. The distance between the building and the palm tree is 4 m.
The distance between the vertices of two branches of a hyperbola is 60 mm. The asymptotes of the curve are inclined at 600 to the transverse axis. Construct the hyperbola.
The distance between the vertices of two branches of a hyperbola is 120 mm. The distance between the vertex and a double ordinate of length 140 mm is 50 mm. Construct the hyperbola. What is the distance between the vertex and the focus?
The ordinate of a point P on the curve is 40 mm and is at a distance of 20 mm from the vertex. Draw the parabola
Draw a straight line AB of any length. Mark a point F, 75 mm from AB. Trace the paths of a point P moving in such a way that the ratio of its distance from the point F, to its distance from AB is 3:2. Plot at least 8 points. Name the curve. Draw a normal and a tangent to each curve at a point on it, 50mm from F.
Draw an ellipse by focus-directrix method when the distance of the focus from the directrix is equal to 60 mm and the eccentricity is 2/3.
In a triangle ABC, AB, AC, and BC are 100 mm, 55 mm and 70 mm respectively. Draw an ellipse and that A and B are foci, and C is a point on the curve. Find directrix and eccentricity of ellipse
Draw a parabola having a base of 80 mm and an axis equal to 80 mm by the tangent method.
A fixed point is 80 mm from a fixed straight line. Draw the locus of a point P moving in such a way that its distance from the fixed straight line is twice its distance from the fixed point. Name the curve.
The major axis of an ellipse is 150 mm long and the minor axis is 100 mm long. Find the foci and draw the ellipse by ‘arcs of circles’ method. Draw a tangent to the ellipse at a point on it 25 mm above the major axis.
Two points A and B are 100mm apart. A point C is 75 mm from A and 60 mm from B. Draw an ellipse passing through A, B and C.
Draw a rectangle having its sides 125 mm and 75 mm long. Inscribe two parabolas in it with their axis bisecting each other and having common axis.
Two straight lines OA and OB make an angle of 750 between them. P is a point 40 mm from OA and 50 mm from OB. Draw a hyperbola through P, with OA and OB as asymptotes, making at least ten points
The major axis of an ellipse is 150mm long with P as its mid point. The foci of ellipse are 50mm away from mid point .Draw the ellipse.
The vertex of a hyperbola is 80mm from its focus. Draw the curve if the centricity is 4/3. Draw a normal and tangent at a point on the curve, 75mm from the directrix.
A ball hit by a bat travels a distance of 100meters with a height of 50meters.Trace the path of the ball.
The major axis of an ellipse is 200mm long and the minor axis is 150mm long. Find the foci and draw the ellipse by concentric circles method
In a triangle ABC; AB, AC and BC are 75 mm, 60 mm and 50 mm respectively. Draw an ellipse such that A and B are the foci and C is a point on the curve.
A fixed point is at 50 mm from a fixed straight line. Draw the curves when eccentricity is
(a) 1 and
Name the curves. Draw tangents and normals to the curves through a point P, 60mm from the straight line.
Construct a rectangular hyperbola, when a point P on it is at a distance 30 mm and 40 mm from two asymptotes. Also, draw a tangent to the curve at a point 35 mm from an asymptotes.