" 6."(x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If a point (x_(1),y_(1)) lies in the shaded region (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, shown in the figure,then (x^(2))/(a^(2))-(y^(2))/(b^(2))<0 statement 2: If P(x_(1),y_(1)) lies outside the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, then (x_(1)^(2))/(a^(2))-(y_(1)^(2))/(b^(2))<1

If (x)/(a)-(y)/(b) tan theta =1 and (x)/(a) tan theta +(y)/(b)=1 , then the value of (x^(2))/(a^(2))+(y^(2))/(b^(2)) is

The equation of the ellipse with its centre at (1, 2), focus at (6, 2) and passing through the point (4 ,6) is (x-1)^(2)/a^(2)+(y-2)^(2)/b^(2)=1, then

Prove that the locus of the middle points of normal chords of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 is the curve (x^(2)/a^(2)+y^(2)/b^(2))(a^(6)/x^(2)+b^(6)/y^(2))=(A^(2)-B^(2))^(2)

Statement 1:If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x_1^ 2)/(a^2)-(y_1 ^2)/(b^2)<1

If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x1 2)/(a^2)-(y1 2)/(b^2)<1

If x/a costheta+y/b sintheta=1 and x/a sintheta-y/bcostheta=1 Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2