Find the equation of the tangent to the ellipse `x^2/a^2+y^2/b^2=1` at (x= 1,y= 1)`.

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.

Find the eqauations of the tangent to the ellipse 4x^(2)+9y^(2)=36 at the point (x_(1),y_(1)) , hence find the coordinates of the points on this ellipse at which the tangents are parallel to the line 2x-3y=6

Find the equations of the tangents to the ellipse 2x^2 + 3y^2 = 30 , which are parallel to the straight line x + y + 18 = 0.

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at ( a sec, theta b tan theta) . Hence show that if the tangent intercepts unit length on each of the coordinate axis than the point (a,b) satisfies the equation x^(2)-y^(2)=1

Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1) .

Find the equations of the tangent and the normal to 16 x^2+9y^2=144 at (x_1,\ y_1) where x_1=2 and y_1>0 .

Find the equation of the tangent to the ellipse 2x^(2)+3y^(2)=30 , which are parallel to the straight line x+y+18=0

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot

Find the equations of the tangents ot the ellipse x^(2)+3y^(2)=4 which are perpendicular to x+2y+7=0 .

The equation of the tangent to the conic x^(2)-y^(2)-8x+2y+11=0 at (2,1) is