If (`a x^2+c)y+(a x^2+c )=0a n dx` is a rational function of `ya n da c` is negative, then `a c^(prime)+c^(prime)c=0` b. `a//a '=c//c '` c. `a^2+c^2=a^('2)+c^('2)` d. `a a^(prime)+cc^(prime)=1`

If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function of y and ac is negative, then a. a c^(prime)+c^(prime)c=0 b. a//a '=c//c ' c. a^2+c^2=a^('2)+c^('2) d. a a^(prime)+c c^(prime)=1

If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function of y and ac is negative, then a. a c^(prime)+c^(prime)c=0 b. a//a '=c//c ' c. a^2+c^2=a^('2)+c^('2) d. a a^(prime)+c c^(prime)=1

If (ax^(2)+c)y+(a'x^(2)+c')=0 and x is a rational function of y and ac is negative,then ac^(+)+c'c=0 b.a/a'=c/c'c.a^(2)+c^(2)=a^(2)+c^(2) d.aa'+cc'=1

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x^2+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .

Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime) are perpendicular if aa^(prime) + c c^(prime) + 1=0

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|

Fid the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d ' are perpendicular.