`(x^(2))/(r^(2)-r-6)+(y^(2))/(r^(2)-6r+5)=1` will represent an ellipse if r lies in the interval

x^2/(r^2+r-6)+y^2/(r^2-6r+5)=1 will represent the ellipse if r lies in the interval

x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will represent ellipse if r lies in the interval (a).(- oo ,2) (b). (3, oo ) (c). (5, oo ) (d).(1, oo )

The equation (x^2)/(1-r)-(y^2)/(1+r)=1,r >1, represents (a)an ellipse (b) a hyperbola (c)a circle (d) none of these

for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

Let S={(x,y) in R^(2):(y^(2))/(1+r)-(x^(2))/(1-r)=1} , where r ne pm 1 . Then S represents:

If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval in which y lies.

If the circle x^(2)+y^(2)-2x-6y = r^(2)-10 is tangent to the line 12y = 60 , the value of r is

If .^(6)P_(r): .^(6)P_(5) = 1:2 , find the value of r.

"If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y_(2)+xy_(1) is (where y_(r) represents the rth derivative of y w.r.t. x)