If the line hx + ky = 1 touches `x^(2)+y^(2)=a^(2)`, then the locus of the point (h, k) is a circle of radius

If the line hx+ky=(1)/(a) touches the circle x^(2)+y^(2)=a^(2) then the locus of (h,k) is circle of radius

If the pair of lines joining the origin and the points of intersection of the line ax+by=1 and the curve x^(2)+y^(2)-x-y-1=0 are at right angles, then the locus of the point (a, b) is a circle of radius=

Through a fixed point (h,k) secants are drawn to the circle x^(2)+y^(2)=r^(2). Then the locus of the mid-points of the secants by the circle is

If the line y=mx+asqrt(1+m^2) touches the circle x^2+y^2=a^2 , then the point of contact is

If the line y=sqrt(3)x+k touches the circle x^(2)+y^(2)=16, then find the value of k

Through a fixed point (h,k), secant are drawn to the circle x^(2)+y^(2)=r^(2) . Show that the locus of the midpoints of the secants by the circle is x^(2)+y^(2)=hx+ky .

Through a fixed point (h,k), secant are drawn to the circle x^(2)+y^(2)=r^(2) . Show that the locus of the midpoints of the secants by the circle is x^(2)+y^(2)=hx+ky .

Through a fixed point (h,k), secant are drawn to the circle x^(2)+y^(2)=r^(2) . Show that the locus of the midpoints of the secants by the circle is x^(2)+y^(2)=hx+ky .