Find the locus of the point of intersection of lines `xcosalpha+ysinalpha=a` and `xsinalpha-ycosalpha=b(alpha` is a variable).

(2, 1) is the points of intersection of two lines

Prove that for all values of theta , the locus of the point of intersection of the lines xcostheta+ysintheta=a and xsintheta-ycostheta=b is a circle.

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

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.

If alpha-beta= constant, then the locus of the point of intersection of tangents at P(acosalpha,bsinalpha) and Q(acosbeta,bsinbeta) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is: (a) a circle (b) a straight line (c) an ellipse (d) a parabola

The locus of the point of intersection of perependicular tangent of the parabola y^(2) =4ax is

Find the locus of the point of intersection of the normals at the end of the focal chord of the parabola y^2=4a xdot

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

If the line ax+ by =1 passes through the point of intersection of y =x tan alpha + p sec alpha, y sin(30^@-alpha)-x cos (30^@-alpha) =p , and is inclined at 30^@ with y=tan alpha x , then prove that a^2 + b^2 = 3/(4p^2) .