Show that the tangent of an angle between the lines `(x)/(a)+(y)/(b)=1` and `(x)/(a)-(y)/(b)=1` and `(2ab)/(a^(2)-b^(2))`.

Show that the tangent of an angle between the lines x/a+y/b=1 and x/a-y/b=1\ i s(2a b)/(a^2-b^2)

The equation of a bisector of the angle between the lines y-q=(2a)/(1-a^(2))(x-p)and y-q=(2b)/(1-b^(2))(x-p) is

Show that the acute angle between the asymptotes of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a^2> b^2), is 2cos^(-1)(1/e), where e is the eccentricity of the hyperbola.

Show that the area included between the parabolas y^2 = 4a(x + a) and y^2 = 4b(b - x) is 8/3 sqrt(ab) (a+b).

Find the equation of the tangent to the curve (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,\ y_1) on it.

Solve : {:((a)/(x)-(b)/(y)=0),((ab^(2))/(x)+(a^(2)b)/(y)=a^(2)+b^(2)):}

Show that the angle between the asymptotes of the hyperola (x^(2))/a^(2) -y^(2)/b^(2)=1" is "2Tan^(-1) (b/a) or 2 sec^(-1) (e ) .

Show that the tangents drawn at those points of the ellipse (x^(2))/(a)+(y^(2))/(b)=(a+b) , where it is cut by any tangent to (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , intersect at right angles.

Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2