If a tangent of slope `2` of the ellipse `(x^2)/(a^2) + (y^2)/1 = 1` passes through the point `(-2,0)`, then the value of `a^2` is equal to

If a tangent of slope 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is normal to the circle x^2+y^2+4x+1=0 , then the maximum value of a b is

If a tangent of slope 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is normal to the circle x^2+y^2+4x+1=0 , then the maximum value of a b is

A tangent of slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(1)=1 passes through (-2, 0) . Then, three times the square of the eccentricity of the ellipse is equal to

A tangent of slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(1)=1 passes through (-2, 0) . Then, three times the square of the eccentricity of the ellipse is equal to

If m_(1) and m_(2) are slopes of the tangents to the ellipse (x^(2))/(16)+(y^(2))/(9)=1 which passes through (5, 4), then the value of (m_(1)+m_(2))-(m_(1)m_(2)) is equal to

If m_(1) and m_(2) are slopes of the tangents to the ellipse (x^(2))/(16)+(y^(2))/(9)=1 which passes through (5, 4), then the value of (m_(1)+m_(2))-(m_(1)m_(2)) is equal to

Find the equation of the tangent to the ellipse : x^2/5+y^2/4=1 passing through the point (2,-2) .

If a tangent of slope 2 of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is the normal to the circle x^(2)+y^(2)+4x+1=0 then the maximum value of a.b is equal to