Show that the for all values of `theta,xsintheta-y=costheta=a` touches the circle `x^(2)+y^(2)=a^(2)`

Tangent to the parabola y=x^(2)+ax+1 at the point of intersection of the y-axis also touches the circle x^(2)+y^(2)=r^(2) . Also, no point of the parabola is below the x-axis. The radius of circle when a attains its maximum value is

For what value of lamda will the line y=2x+lamda be tangent to the circle x^(2)+y^(2)=5 ?

For what value of lambda does the line y=2x+lambda touches the hyperbola 16x^(2)-9y^(2)=144 ?

If x cos theta- y sin theta=a,x sin theta+ y cos theta=b , prove that x^2+y^2= a^2+b^2 .

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 .

If x costheta-ysintheta=a and xsintheta+ycostheta=b , then prove that x^2+y^2=a^2+b^2 .

The values of lamda for which the line y=x+ lamda touches the ellipse 9x^(2)+16y^(2)=144 , are

If xsin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta, prove that x^2+y^2=1

Minimum value of cos2theta+costheta for all real value of theta is

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 . Find the coordinates of the point of contact.