The ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and the straight line `y=mx+c` intersect in real points only if:

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the straight line y=mx^(2)+c intersect in real points only if:

The straight line y=mx+c cuts the circle x^2+y^2=a^2 at real points if

The line x= t^(2) meet the ellipse x^(2) +(y^(2))/( 9) =1 in the real and distinct points if and only if

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2=1 at the points where it is intersected by the line 2x+3y=1 . The point of intersection of these tangents is (8, 6). Statement 2 : The equation of the chord of contact to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from an external point is given by (x x_1)/(a^2)+(y y_1)/(b^2)-1=0

Show that the tangent to the ellipse x^2/a^2+y^2/b^2=1 at points whose eccentric angles differ by pi/2 intersect on the ellipse x^2/a^2+y^2/b^2=2

" Eccentricity of ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 " such that the line joining the foci subtends a right angle only at two points on ellipse is "

The locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ( b < a) (a) is a an circle (b) ellipse (c) hyperbola (d) pair of straight lines

The locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ( b < a) (a) is a an circle (b) ellipse (c) hyperbola (d) pair of straight lines

The line x=at^(2) meets the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in the real points if