Equation of a normal to the given ellipse whose slope is 'm' is `y=ma-+((a^2-b^2)m)/sqrt(a^2+b^2m^2)`

The equation of the normal to the curve y^2=4ax having slope m

Equation of normal to the parabola y^(2)=4ax having slope m is

The equation of ellipse whose focus is (0, sqrt(a^(2) -b^(2) ) ) , directrix is y = (a^(2))/( sqrt(a^(2) -b^(2)) and eccentricity is ( sqrt(a^(2) -b^(2)) )/( a ) is

Find the equations of the bisectors of the angles formed by the following pairs of lines : y-b= (2m)/(1-m^2)(x-b) and y-b= (-2m)/(1-m^2)(x+b)

Equation of a bisector of the angle between the line y-b=(2m)/(1-m^2)(x-a) and y-b=(2m')/(1-m^2)(x-a) is

Find the equations of the tangent and the normal to the given curve at the indicated point : y^(2) = 4ax " at " ((a)/(m^(2)), (2a)/(m))

The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) and my-x=sqrt(a^2+b^2m^2) is

The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) and my-x=sqrt(a^2+b^2m^2) is

The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) and my-x=sqrt(a^2+b^2m^2) is

The line l x+m y+n=0 is a normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . then prove that (a^2)/(l^2)+(b^2)/(m^2)=((a^2-b^2)^2)/(n^2)