" 15."(x^(2))/(a^(2))-(y^(2))/(b^(2))=1

A : The eqution of the normal to the hyperbola x^(2) -4y^(2) =5 at (3,-1) is 4x -3y = 15 R : The equation of the normal to the hyperbola (x^(2))/( a^(2))-(y^(2))/(b^(2)) =1 at (x_1,y_1) "is" ( a^(2)x)/( x_1) +(b^(2)y)/( y_1) =a^(2) +b^(2)

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

Many properties of an ellipse in the standard form (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 can be used easily in the general form also. Consider an ellipse with the equation (15x-3)^(2)+(15y+5)^(2)=(12x+5y-2)^(2) . Find the eccentricity of the ellipse.

Many properties of an ellipse in the standard form (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 can be used easily in the general form also.Consider an ellipse with the equation. (15x-3)^(2)+(15y+5)^(2)=(12x+5y-2)^(2) Q) Eccentricity of the ellipse ywill be?

If cos ^(-1)\ (x)/(a) + cos^(-1)\ (y)/(b) = theta , then (x^(2))/(a^(2)) +(y^(2))/(b^(2))=?

For the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 and (x^(2))/(b^(2))+(y^(2))/(a^(2)) =1