Show that the straight line `xcosalpha+ysinalpha=p` touches the curve `x y=a^2,` if `p^2=4a^2cosalphasinalphadot`

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2cos^2alpha+b^2sin^2alpha=p^2dot

Show that xcosalpha+ysinalpha=p touches the parabola y^2=4a x if pcosalpha+asin^2alpha=0 and that the point of contact is (atan^2alpha,-2atanalpha)dot

Show that the straight line x-2y+3=0 and 6x+3y+8=0 are perpendicular .

If we reduce 3x+3y+7=0 to the form xcosalpha+ysinalpha=p , then find the value of pdot

The equation of the straight lines which are both tangent and normal to the curve 27x^(2)=4y^(3) are

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.

The number of values of c such that the straight line y=4x+c touches the curve (x^2)/4+(y^2)/1=1 is 0 (b) 1 (c) 2 (d) infinite

Find the equation of the straight lines touching both x^2+y^2=2a^2 and y^2=8a xdot

If the straight lines y/2=x-p and ax+5=3y are parallel , then find "a" .