`x=acostheta+bsintheta`, `y=asintheta-bcostheta`, find `(dy)/(dx)`

lf x=acostheta+bsintheta , y=asintheta-bcostheta then show that y^2(d^2y)/dx^2-x dy/dx+y=0

x=acostheta+bsintheta and y=asintheta-bcostheta, show that y^2(d^2y)/(dx^2)-x(dy)/(dx)+y=0

The radius of the circle whose equation in parametric form is P(theta)=(acostheta+bsintheta,asintheta-bcostheta), is : (a+b)/2 (b) sqrt(a b) sqrt(a^2+b^2) (d) (a b)/(a+b)

(i) Find the equation a circle passing through the point (2+3costheta,1+3sintheta) where 'theta' is a parameter. (ii) Prove that the equations x=acostheta+bsintheta and y=asintheta-bcostheta represents a circle.

If x=acostheta-bsinthetaandy=asintheta+bcostheta , then show that : x^(2)+y^(2)=a^(2)+b^(2)

Show that the normal at any point theta to the curve x=acostheta+athetasintheta,\ y=asintheta-a\ thetacostheta is at a constant distance from the origin.

If acostheta+bsintheta=4 and asintheta-bcostheta=3 , then a^2+b^2 = (a) 7 (b) 12 (c) 25 (d) None of these

If acostheta+bsintheta=m and asintheta-bcostheta=n , then a^2+b^2= (a) m^2-n^2 (b) m^2n^2 (c) n^2-m^2 (d) m^2+n^2

If acostheta+bsintheta=m and asintheta-bcostheta=n , then show that a^(2)+b^(2)=m^(2)+n^(2) .

i) If acostheta+bsintheta=m and asintheta-bcostheta=n , then prove that: a^(2)+b^(2)=m^(2)+n^(2)