The ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the straight line $y = mx + c$ intersect in real points only if
The ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the straight line $y = mx + c$ intersect in real points only if
- A
${a^2}{m^2} < {c^2} - {b^2}$
- B
${a^2}{m^2} > {c^2} - {b^2}$
- C
${a^2}{m^2} \ge {c^2} - {b^2}$
- D
$c \ge b$
Similar Questions
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $36 x^{2}+4 y^{2}=144$
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $36 x^{2}+4 y^{2}=144$
If the length of the latus rectum of an ellipse is $4\,units$ and the distance between a focus and its nearest vertex on the major axis is $\frac {3}{2}\,units$ , then its eccentricity is?
If the length of the latus rectum of an ellipse is $4\,units$ and the distance between a focus and its nearest vertex on the major axis is $\frac {3}{2}\,units$ , then its eccentricity is?
- [JEE MAIN 2018]
If $x = 9$ is the chord of contact of the hyperbola ${x^2} - {y^2} = 9$, then the equation of the corresponding pair of tangents is
If $x = 9$ is the chord of contact of the hyperbola ${x^2} - {y^2} = 9$, then the equation of the corresponding pair of tangents is
- [IIT 1999]
The eccentricity of the ellipse $25{x^2} + 16{y^2} - 150x - 175 = 0$ is
The eccentricity of the ellipse $25{x^2} + 16{y^2} - 150x - 175 = 0$ is
The equation $\frac{{{x^2}}}{{2 - r}} + \frac{{{y^2}}}{{r - 5}} + 1 = 0$ represents an ellipse, if
The equation $\frac{{{x^2}}}{{2 - r}} + \frac{{{y^2}}}{{r - 5}} + 1 = 0$ represents an ellipse, if