Prove that for all real values of `xa n dy ,x^2+2x y+3y^2-6x-2ygeq-11.`

Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real values of xa n dy ,t h e nx must lie between 1 and 3 and y must lie between-1/3 and 1/3.

Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real values of xa n dy ,t h e nx must lie between 1 and 3 and y must lie between-1/3 and 1/3.

Prove that graphs y=2x-3a n dy=x^2-x never interest.

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

For all real values of aa n db , lines (2a+b)x+(a+3b)y+(b-3a)=0 and m x+2y+6=0 are concurrent. Then m is equal to______

For the smallest positive values of xa n dy , the equation 2(sinx+sin y)-2cos(x-y)=3 has a solution, then which of the following is/are true? (a) sin(x+y)/2=1 (b) cos((x-y)/2)=1/2 (c)number of ordered pairs (x , y) is 2 (d)number of ordered pairs (x , y)i s3

Prove that graphs of y=x^2+2a n dy=3x-4 never intersect.

Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real x and ydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then a) f(x) is positive for all real x b) f(x) is negative for all real x c) f(x)=0 has real roots d) Nothing can be said about the sign of f(x)

Find the angle of intersection of y=a^xa n dy=b^x

Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dcotx+coty=2