If the normal at the point `P( theta)` to the ellipse `(x^(2))/(14)/(y^(2))/(5)=1` intersects it again at the point Q `(2 , theta)` then ` cos theta` is equal to

Find the focal distance of point P(theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The normal at a point P(theta) on the ellipse 5x^(2)+14y^(2)=70 cuts the curve again at a point Q(2 theta) then cos thetahat I

If the normal at theta on (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b) intersects the curve again at phi then

If P(theta) and Q((pi)/(2)+theta) are two points on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 then find the locus of midpoint of PQ

If P and Q are points with eccentric angles theta and (theta+(pi)/(6)) on the ellipse (x^(2))/(16)+(y^(2))/(4)=1 , then the area (in sq. units) of the triangle OPQ (where O is the origin) is equal to

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is

If the length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

If a tangent and a normal to the ellipse x^(2)+4y^(2)=4 at the point theta meets its major axis at P and Q such that PQ=2 then (1+cos theta)/(2)=

The points P,Q,R are taken on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentric angles theta,theta+a,theta+2a, then area of ,Delta PQR is independent of