Ellipse frac{{{x^2}}}{{{a^2}}} + frac{{{y^2}}}{{{b^2}}} = 1 and straight line y = mx + c intersect i

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10-2. Parabola, Ellipse, Hyperbola

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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

$c \ge b$

Solution

(c) To cut at real points, ${c^2} \le {a^2}{m^2} + {b^2}$

==> ${a^2}{m^2} \ge {c^2} – {b^2}$.

Standard 11

Mathematics

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