Tangents at right angle are drawn to the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1`. Show that the focus of the middle points of the chord of contact is the curve `(x^(2)/a^(2)+y^(2)/b^(2))^(2)=(x^(2)+y^(2))/(a^(2)+b^(2))`.

Show that the locus of middle points of a focal chord of an ellipe (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is (x^(2))/(a^(2))+(y^(2))/(b^(2))=(ex)/(a)

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

Prove that the locus of the middle points of normal chords of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 is the curve (x^(2)/a^(2)+y^(2)/b^(2))(a^(6)/x^(2)+b^(6)/y^(2))=(A^(2)-B^(2))^(2)

Chords of the circle x^(2)+y^(2)=a^(2) toches the hyperbola x^(2)/a^(2)-y^(2)//b^(2)=1 . Prove that locus of their middle point is the curve (x^2 +y^2)^2=a^(2)x^(2)-b^(2)y^(2)

Find the locus of the middle points of the chords of contact of tangents to the circle x^(2)+y^(2)=1 drawn from the the circle x^(2)+y^(2)+4x+6y+9=0

The line xcosalpha+ysinalpha=p is a tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 . The point of contact is

The locus of the middle points of the portions of the tangents of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the axis is the curve (a) (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(4) (b) quad (a^(2))/(x^(2))+(b^(2))/(y^(2))=4 (c) a^(2)x^(2)+b^(2)y^(2)=4 (d) b^(2)x^(2)+a^(2)y^(2)=4

If the locus of the mid points of the chords of the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1 , drawn parallel to y=m_1x is y=m_2x then m_1m_2=