Prove that the greatest value of `x y` is `c^3/sqrt(2a b)`, if `a^2x^4+b^2y^4=c^6dot`

Prove that the greatest value of x y is c^3//sqrt(2a b)dot if a^2x^4+b^4y^4=c^6dot

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

If sqrt(a+i b)=x+i y ,\ then possible value of sqrt(a-i b) is a. x^2+y^2 b. sqrt(x^2+y^2) c. x+i y d. x-i y e. sqrt(x^2-y^2)

If 3/4 y =6-1/3c, then what is the value of 2x + 9/2y ?

Consider a circle x^2+y^2+a x+b y+c=0 lying completely in the first quadrant. If m_1a n dm_2 are the maximum and minimum values of y/x for all ordered pairs (x ,y) on the circumference of the circle, then the value of (m_1+m_2) is (a) (a^2-4c)/(b^2-4c) (b) (2a b)/(b^2-4c) (c) (2a b)/(4c-b^2) (d) (2a b)/(b^2-4a c)

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , then the minimum possible value of c is (a) -sqrt(2) (b) sqrt(2) (c) 2 (d) 1

Prove that the value of each the following determinants is zero: |[(a^x+a^(-x))^2,(a^x-a^(-x))^2 ,1],[(b^y+b^(-y))^2,(b^y-b^(-y))^2 ,1],[(c^z+c^(-z))^2,(c^z-c^(-z))^2, 1]|

Let x ,y ,z ,t be real numbers x^2+y^2=9, z^2+t^2=4 , and xt-y z=6 Then the greatest value of P=xz is a. 2 b. 3 c. 4 d. 6

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisector of the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6