Q. Show that the feet of normals from a point (h, K) to the ellipse `x^2/a^2+y^2/b^2=1` lie on a conic which passes through the origin & the point `(h, k)`

Q.Show that the feet of normals from a point (h,K) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 lie on a conic which passes through the origin varepsilon the point (h,k)

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

If the normal from the point P(h,1) on the ellipse (x^(2))/(6)+(y^(2))/(3)=1 is perpendicular to the line x+y=8 ,then the value of h is

If the normal at the point P(theta) of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) passes through the origin then

The equation of the ellipse whose centre is at origin and which passes through the points (-3,1) and (2,-2) is

The feet of the normals to (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 from (h,k) lie on

The locus of the mid-points of the chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which pass through the positive end of major axis,is.

The equation of the curve, slope of whose tangent at any point (h, k) is 2k/h and which passes through the point (1, 1) is