Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude.

Find the locus of the vertex of a triangle whose, sum of base angles is fixed.

Describe : The locus of the centres of all circles that are tangent to both the arms of a given angle.

The locus of vertices of all isosceles triangles having a common base.

Describe : The locus of the mid-points of all chords parallel to a given chord of a circle.

Altitudes the perpendiculars drawn from the vertices of a triangle to the opposite side are known as the altitudes of the triangle.

An altitutde of a triangle is five –thirds the length of its corresponding base. If the altitude were increased by 4 cm and the base be decreased by 2 cm, the area of the triangle would remain the same. Find the base and the altitude of the triangle.

Describe the locus of points at distances less than 3 cm from a given point.

Describe the locus of point at distances less than or equal to 2.5 cm from a given point.

Describe the locus of points at distances greater than or equal to 35 mm from a given point.

With a given point and line as focus and directrix, a series of ellipses are described. The locus of the extremities of their minor axis is an ellipse (b) a parabola a hyperbola (d) none of these