Find the normal to the ellipse `(x^2)/(18)+(y^2)/8=1` at point (3, 2).

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.

If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (X_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x+y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

If the straight line 4ax+3by=24 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (agtb) , then find the the coordinates of focii

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1).

Find the equation of normal to the hyperbola x^2-9y^2=7 at point (4, 1).

Find the points on the ellipse (x^2)/4+(y^2)/9=1 on which the normals are parallel to the line 2x-y=1.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.