[(2^(2))/(a^(2))+(y^(2))/(b^(2))=7],[n=0,n=ae]

If straight line lx+my+n=0 is a tangent of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then prove that a^(2)l^(2)+b^(2)m^(2)=n^(2)

If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , show that a^(2) l^(2)-b^(2)m^(2)=n^(2) .

If the line lx+my+n=0 s a tangent to the hyperboal (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then show that a^(2)l^(2)-b^(2)m^(2)=n^(2)

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then show a^2 l^2 - b^2 m^2 =n^2

If y=Ae^(-kt)cos(pt+c), then prove that (d^(2)y)/(dt^(2))+2k(dy)/(dx)+n^(2)y=0, where n^(2)=p^(2)+k^(2)

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0

Find the angle of intersection of the following curves : y^2=xa n dx^2=y y=x^2a n dx^2+y^2=20 2y^2=x^3a n dy^2=32 x x^2+y^2-4x-1=0a n dx^2+y^2-2y-9=0 (x^2)/(a^2)+(y^2)/(b^2)=1a n dx^2+y^2=a b x^2+4y^2=8a n dx^2-2y^2=2 x^2=27ya n dy^2=8x x^2+y^2=2xa n dy^2=x y=4-x^2a n dy=x^2

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 , is ((-a^2l)/n ,(b^2m)/n) (b) ((-a^2l)/m ,(b^2n)/m) ((a^2l)/m ,(-b^2n)/m) (d) ((a^2l)/m ,(b^2n)/m)

If y= Ae^(mx) + Be^(nx) , show that (d^(2)y)/(dx^(2))- (m + n) (dy)/(dx) + mny= 0