Find the slope of normal to the ellipse...

Find the slope of normal to the ellipse , `(x^(2))/(a^(2))+(y^(2))/(b^(2))=2` at the point (a,b).

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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.

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Find the area of the region bounded by the ellipse (x^(2) )/( a^(2)) +( y^(2))/( b^(2))=1

If y=mx+c is the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at any point on it, show that c^(2)=a^(2)m^(2)+b^(2). Find the coordinates of the point of contact.

Find the coodition that the straight line lx+my+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

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