Find the locus of the point at which two given portions of the straight line subtend equal angle.

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0)dot

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is a/an (a)ellipse (b) parabola (c)straight line (d) none of these

Find the number of point of intersection of two straight lines .

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The length of portion of straight line inside the triangle may lie in the range

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The length of portion of straight line inside the triangle may lie in the range

A straight line moves so that the product of the length of the perpendiculars on it from two fixed points is constant. Prove that the locus of the feet of the perpendiculars from each of these points upon the straight line is a unique circle.

Find the locus of the middle point of the portion of the line xcosalpha+ysinalpha=p which is intercepted between the axes, given that p remains constant.

Find the locus of thepoint of intersection of two normals to a parabolas which are at right angles to one another.

Find the locus of the point of intersection of tangents to the ellipse if the difference of the eccentric angle of the points is (2pi)/3dot