Equation of the tangent to `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b)` at the end of latus rectum in the first quadrant is

Portion of asymptote of hypebola (x^(2))/(a^(2)) - (y ^(2))/(b ^(2)) =1 (between centre and the tangent at vertex) in the first quadrant is cut by the y + lamda (x -b) = 0 (lamda is a parameter then

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 value of a for the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b), if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola x^(2)=2(y-2) is

If equation of tangent to ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at (3,(-9)/(2)) is x-2y=12. Then length of latus rectum is

Focus of a parabola y^(2) = 4ax coincides with the focus of the hyperbola 9x^(2) - 16y^(2) = 144 which is on the positive direction of X-axis . Find the equation of the tangent line to the parabola at the end of the latus rectum I which lies in the first quadrant .

Tangents are drawn to the ellipse (x^(2))/(9)+(y^(2))/(5)=1 at the end of latus rectum. Find the area of quadrilateral so formed

For the ellipse (x^(2))/(4) + (y^(2))/(3) = 1 , the ends of the two latus rectum are the four points

Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose latus rectum is half of its major axis.(a>b)

From the point (2,2) tangent are drawn to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1. Then the point of contact lies in the first quadrant (b) second quadrant third quadrant (d) fourth quadrant